I didn't even remember my PS4 needs installing because usually I put the disc turn on the PS4 and keep doing other stuff =p

On the downloads as well when I receive PS+ game or buy very cheap when I notice it already downloaded and installed.

I have a 3TB driver, like 100 games installed and still 25% free, never had to uninstall =p

At one point in time the only PS3 I had was a 12 GB. My original PS3 had broke, and I didn't fix or replace it until I needed to. The day Dark Souls 2 came out was the day I decided to remedy the situation, and I did so by opting into the cheapest SKU I could find, and it was a 12 GB Super Slim, which I think was around $200 at the time, plus the cost of the Dark Souls 2 game.

I really regret that purchase. The 12 GB limit sucks, but even worse than that is the fact that the damn thing started crapping out on me after less than a year. The system still works, but every so often the fan within the system will become extremely loud... and I mean LOUD... Something is loose and it's probably a simple fix but I haven't bothered to acquire the tools to do so. (Since then I bought a co-workers PS3 for $50 along with controllers and a dozen or so games a couple years ago).

I have an OG 500gb PS4 still and I have no problem whatsoever, and I have a ton of physical games. Maybe I'm just using it more efficiently, and many here have already posted great options that could suit your gaming habits.

I don't see the problem.
I'm sure there is a mode where the PS4 can download updates when it's turned off.
Another solution would be to play offline. No updates needed.

And I find it hilarious how people still bitch on install times. You aren't forced to sit in front of the console and watch the install bar to go up. Play or do something else! It doesn't take a huge amount of time.
Also doesn't the PS4 now also support external HDDs? Just plug in one of those and keep all of your favourite games there. I have got around 20 HDDs flying around. Many aren't even in use as they are too small for my needs and I've updgraded them to 4TB and 5TB.
Still, even small ones that are only 500GB or 1TB are enough for that task and can be found for example in old laptops.

You can adjust PS4 to download games in your queue and also update any game installed while your console is either on or in sleep mode.

Certainly if you have a lot of games, a 500GB HDD and don't want to delete games you may have some problems, otherwise is just a matter of planning.

Worse case, I gone there on launch and purchased a game like RDR that take almost 2 hours to install I would just watch a movie while it install.

The switch

This doesn't bother me too much but its because I've got 1 1TB PS4 for myself. I'm never playing more than 4 games at a time so uninstalling/reinstalling games is never an issue for me.

patches typically download in sleep mode or in the background so it's also not an issue for me. 

One thing that has suprirsed me was loading times & general lack of speed of the OS.

Hopefully next gen SSD sorts both of these issues out.

That's some crazy 1st world problems ya got there...good luck.

The biggest problem I have with my PS4 is just that the OS is so incredibly slow. I also really don't like the fact that something like every 1 in 7 times I start my PS4 Pro, it has a 1-2 second delay in sound and so I have to restart it again.

Internal or external? I'd like a 3TB internal drive, so if you have one tell me where you got it!