"Playstation is still more affordable than Switch unless you only buy games on release"

For the most part, no, this is wrong.  First there is the very obvious $500 for PS5 vs. $300/$350 for Switch.  Secondly, third party games on Switch do tend to come down in price.  It is mostly the first party games that stay high in price and even there Nintendo runs discounts regularly for people who want that.

Nintendo only make discounts for a very specific number of titles that aren't moving many copies anymore and for a very limited time, generally on holidays and the discounts are never under 40 USD. Meanwhile if you get a Playstation you can buy almost anything in the library for less than 30 USD, or not buy at all, just subscribe for Ps Plus. Switch has less expensive hardware but software expenses clearly offset this down the line unless you're the kind of gamer that but maybe one game a year and always close to launching. 

I'm not saying this in a negative way at all, if something it only highlights how successful the Switch is. Just to state your idea that Switch is an inexpensive console makes very little sense.

I can see Switch being a less expensive option though if you have multiple devices to share the same physical games, in this point I can see an advantage for Switch as you can have one without the expenses of getting a new TV to play, but this in no way resembles how PS1/PS2 used to be consumed. If anything is something more related to handhelds than with any stationary consoles

I'll proceed by stating the obvious: as far as gaming library goes, the successor of PS1/PS2 is the PS5. The switch is the successor of Wii and DS. 

Nintendo only make discounts for a very specific number of titles that aren't moving many copies anymore and for a very limited time, generally on holidays and the discounts are never under 40 USD. Meanwhile if you get a Playstation you can buy almost anything in the library for less than 30 USD, or not buy at all, just subscribe for Ps Plus. Switch has less expensive hardware but software expenses clearly offset this down the line unless you're the kind of gamer that but maybe one game a year and always close to launching. 

I'm not saying this in a negative way at all, if something it only highlights how successful the Switch is. Just to state your idea that Switch is an inexpensive console makes very little sense.

I can see Switch being a less expensive option though if you have multiple devices to share the same physical games, in this point I can see an advantage for Switch as you can have one without the expenses of getting a new TV to play, but this in no way resembles how PS1/PS2 used to be consumed. If anything is something more related to handhelds than with any stationary consoles

I'll proceed by stating the obvious: as far as gaming library goes, the successor of PS1/PS2 is the PS5. The switch is the successor of Wii and DS. 

Nintendo only make discounts for a very specific number of titles that aren't moving many copies anymore and for a very limited time, generally on holidays and the discounts are never under 40 USD. Meanwhile if you get a Playstation you can buy almost anything in the library for less than 30 USD, or not buy at all, just subscribe for Ps Plus. Switch has less expensive hardware but software expenses clearly offset this down the line unless you're the kind of gamer that but maybe one game a year and always close to launching. 

I'm not saying this in a negative way at all, if something it only highlights how successful the Switch is. Just to state your idea that Switch is an inexpensive console makes very little sense.

I can see Switch being a less expensive option though if you have multiple devices to share the same physical games, in this point I can see an advantage for Switch as you can have one without the expenses of getting a new TV to play, but this in no way resembles how PS1/PS2 used to be consumed. If anything is something more related to handhelds than with any stationary consoles

I'll proceed by stating the obvious: as far as gaming library goes, the successor of PS1/PS2 is the PS5. The switch is the successor of Wii and DS. 

Your view assumes that everyone else's gaming habits are like yours.  I.e. if a person doesn't buy games at release, but they do buy a lot of games, then PS5 is cheaper than Switch.  What you are describing is actually niche behavior.  It is possible for a person to pay less on PS5 than Switch and play the same amount of games.  However, most of the time Switch is cheaper than PS5 even when taking all expenses into account and not just hardware.

-If a person buys hardware and only a few games, then Switch is cheaper.
-If a person mostly buys new releases, then Switch is cheaper, because PS5 new releases are $70 vs. $60 for Switch.  (Keep in mind that for most games the majority of sales happen during the first couple of months when the game is at full price.)
-If a person gets an online subscription and mostly plays games via that (either online multiplayer games or games free with the subscription), then PS5 is more expensive, because the subscription is a lot more expensive.
-If a person wants a system where they play games with friends, then they can potentially save a ton of money on Switch, because local multiplayer games like Mario Kart and Smash Bros only require one system, while popular multiplayer games on PS5 are online and require both multiple systems and a subscription.

-If we go by your scenario, where a person buys a ton of games, but waits a while to buy software trying to save as much money as possible, then PS5 is sometimes cheaper, but often Switch is still cheaper.  It is based on several factors though like
1) Which hardware is bought: $400/$500 for PS5 vs $200/$300/$350 for Switch
2) How many games are bought.  If a person saves $10 on average per PS5 game, then it takes 5 games for the systems to cost the same in the best case ($350 vs. $400) and it takes 30 games to break even in the worst case ($200 vs $500).  All of this assumes you are only playing single-player offline games.
3) People can borrow and share games with their friends, and especially do this if they are frugal.
4) PS5 games are more likely to have in game purchases.

It should be obvious at first that PS5 is more expensive than Switch (more expensive hardware and games), and on deeper investigation PS5 is still more expensive than Switch.  This notion that PS5 is cheaper is a niche scenario, and it distracts from the larger point: Playstation is no longer the system that it used to be.  PS1 and PS2 were affordable systems where you could play the latest Japanese games, including Japanese games made by Sony themselves.  Today the system that fits this role is the Switch.  Not only is it a cheaper system, but about 90% of the games sold in Japan today are on the Switch, while Sony has closed down its Japanese studio.  Switch is the affordable system for Japanese games.  Switch is filling the role that PS1 and PS2 originally filled. 

Bold: That's not true. Some of the most often discounted games in Europe are Mario Kart 8 Deluxe, Super Mario Party and NSMBUDX. The only games that absolutely never ever go on sale are mainline Pokémon games and Animal Crossing: New Horizons.

A few times per year around half a dozen to a dozen first party games are discounted and it's always a mixture of big and small sellers. Luigi's Mansion 3, Super Mario Odyssey and Splatoon 2 have also gone on sale quite often. I've also gotten Smash Ultimate on sale. I think only BotW has gone on sale only once when they showed the sequel at E3 2021.

Well I can only speak about Brazil. Splatoon and Mario Odyssey go on sales, but I don't remember about Marik Mart

Zelda was discounted once or twice, I remember. But the games that get discounts more frequently (generally on holidays or discount weeks) are the ones like Pokemon Let's Go, Link's Awakening, Captain Toad and Donkey Kong tropical Freeze 

The major loophole in your reasoning is that anybody actually needs to wait software prices to go down on Playstation, when in reality they don't. Most of people don't buy hardware at launch, they buy on the second half of their life. At this point Playstation already has a extensive library with games well behind 30 USD and often getting discounts to be bought for even less than 20. You don't even need to purchase much more than 6 games for Playstation starting be a more compelling option 

I also wonder if you are aware subscription services from Playstation give you free two to three games monthly for only 5 USD a month. I'm talking about AAA games from big publishers, not ports of fifth gen. 

But that's tangential. The reason why Playstation 4 and 5 are the successors of Playstation 1 and 2 lies on its gaming library. The only Japanese third parties that sold more than 2 million copies that aren't present on Playstation ecosystem are: Monster Hunter Rise and Ocopath Travaler

If you like JP games, Playstation is the path. Otherwise buy an Xbox, it's less expensive have Game Pass and get all western third parties as well

The succes of Switch is due to their absurdly strong first party line up that stretches to a point they will have a mind-blowing number of over 20 games selling over 10 million copies 

Your next argument is "Yes, but Nintendo games are JP games too, mostly"

Sure, they are. But one doesn't need to think much to realize Nintendo games were never on Playstation hardware. So whoever wanted to play Nintendo should have bought Nintendo. This was true in the 90s during the peak of Playstation crazy and this is true now.