I disagree a bit. While I would not overestimate brand loyalty, history also has shown that it exists. Look no further than PS4. At launch the library had a lot of 'definitive ports'. But people bought the system and rebought the games. A friend literally said, he rebought something (don't remember, might have been Tomb Raider) so that he has something to play with his new PS4, while waiting for more games. A lot of PS4 sold on brand loyalty. And the promise of a great library down the road was fulfilled, so I don't see thta brand loyalty destroyed.
But even more counts the network effects Xxain talks about. Network effects are really strong. That is the reason competing with Twitter and Facebook is so hard, people don't want to lose their friends, followers, likes and so on. Same with the friendlist, achievements and more on consoles. And just think about it: you own a PS4 and have PS+. As PS5 releases you might not be interested, but each month you automatically get free games for PS5. The deal looks sweeter as time goes by. Cross-buy means you don't have to rebuy all the smaller download-games you purchased and are available on the new system. And so on. Sony has a lot of this stuff to pull you over to the new system if you are already invested in the previous one.
Nintendo by the way sucks at these effects. Going from Wii to WiiU and 3DS you had to readd your friends. Switch at least offers to send your previous friends an invitation, so it is a bit better. You had always to rebuy all you digital downloads on each Nintendo system, even as the same was available. This was true for virtual console, although I remember Nintendo offered a discount for VC-titles you owned on Wii. Now VC is dropped completely. Miiverse was just canned. Just think about it, if Switch had retained Miiverse, all the WiiU and 3Ds owners would have seen posts and screenshots from games on Switch in their Miiverse. This could have been a pull-factor. So yes, you are right in regards to Nintendo. For Nintendo each new gen starts at zero. But this is a failing of Nintendo, others do that better.
In response to your first paragraph: The plural of anecdote is not data. Of course brand loyalty exists, but the way Xxain and you talk about it overstates it. An anecdote of a PS4 purchase doesn't hold much weight because the alternatives in that generation were very weak. Also, most PS+ subscribers don't download their free games. Even the highly popular Rocket League was downloaded by only about half of the subscribers at the time and that's the best case scenario. Download rates for other games can be expected to be (well) below 10% of active subscribers during any given month, so that's a few million people at best.
What you say about Nintendo consoles should make you realize how little these things matter. The Wii U had full backwards compatibility to retain all digital games and all save data for retail and digital games, but it sold worse than everything else. Switch has no backwards compatibility whatsoever and sells much better than the 3DS. You talk about Miiverse as if it could have been a difference maker, but really, who cares. Nevermind that the abolishment of Miiverse meant that gamers had to share their screenshots and comments on Twitter and Facebook, so even in the context you are using, you'd have to consider the end of Miiverse a positive thing.
Microsoft made big efforts to make the Xbox One backwards compatible and Xbox Live was superior to PSN during the seventh generation, but these things hardly mattered.
The bottom line is that other factors are much, much more important. Don't fall into the trap of "the PS2 owned its generation, so of course the PS3 will be a winner too" or "the 360 has comfortably beaten the PS3 in the USA, so the Xbox brand has America locked down now and in the future." If people don't want to lose their games, saves and achievements, then what they do is keep the old console and buy the new console that they consider the best choice. There's a small portion of the market that is loyal to a brand, but that's not going to turn into a significant amount anytime soon.
But all this is sidetracking. Regardless of this specific discussion, it's clear that the PS5 has to sell at least as well as the PS4 to even have a chance at winning in the ninth generation. That won't be an easy feat when the competition doesn't screw themselves over and that's why the upcoming years will have a lot more console wars than the previous five.