If you read "bad battery design" and just make assumptions about what that means, then maybe thats on you because it only takes the slightest amount of curiosity to say "I wonder why somebody would be talking about having to replace batteries"

I've had both pixel models affected and the 4a at one point was smoking because of a related heat issue with the phone where the charge port overheats. The 4a at least was an easier fix- the screen is easier to remove.

the hardware is completely underpowered

It depends, compared with a gaming rig? Yes, it has been more powerful than a Nintendo Switch since ages ago and although this is not a biggest achievement, remember Switch 1 has a decent lineup almost since its conception (oh, and some even emulate Switch games there).

the display is absolutely tiny

It depends on the phone model, I have been doing fine with my Poco F2 Pro with a 6,67 inches screen, destiny has taken me to a Samsung Galaxy S20 with 6,2 inches and I have been doing just fine, I still prefer the Poco as it didn't have any notch or camera hole whatsoever.

the display resolution is too high

Not sure if I am following this correctly, but AFAIK you can tweak that from settings or developer settings.

the battery is tiny

For smaller devices yeah, it tends to be the norm, but batteries are becoming bigger, so I expect more 3D gaming time if games are optimized.

you're constantly taken out of the game by annoying interruptions

I mean, this is easily fixable with 3rd party or system inbuilt apps... Both of my devices have a gaming mode and it can enable do not disturb any time I open a game, now if you really can't allow to use that feature I understand, I could care less about somebody not been able to reach me by a phone call lol.

going in and out is a pain because the system will kill the app

This depends a lot of the phone, again, and that is correct for my case with the F2 Pro as it only had 6 GB of RAM, the S20 has 8 GB of RAM and I haven't noticed this in a while, and nowadays phones are been shipped with crazy amounts of RAM so yeah...

and worst of all, pretty much every mobile app I've ever seen, as well as the stores that provide them, are absolutely riddled with ads and microtransactions. Back in the day we had Angry Birds, and it was legitimately a fun, excellent, and simple game that I really enjoyed, but that game, and the entire industry as a whole, has been absolutely ruined by exploitation.

This is no secret for anyone, and this only happened because people allowed it and that's why mobile gaming is so popular, for good and bad reasons alike.

That's why in my previous comment I said some companies have been putting games for mobile with quality.

Is there another store that exists that isn't like that where you can find actually fun games to play?

Not sure if it counts as a store, but both Android and Apple offer a subscription tier model which let's you play lots of games without ads or dark patterns, there is also the Netflix subscription games which operate similarly...

Now talking about stores I heard there are some interesting games in Fdroid, and we now have the Epic Game Store, both on Android.

Like I said, I don't really game that much on the phone, but I keep good games in my radar from time to time, and we have some good ones like Balatro, Vampire Survivors, Shattered Pixel Dungeon, etc, I still prefer emulation on Android.

I hop in some Android subreddits on Reddit and you can get a lot of recommendations there (or ask here in Lemmy I guess), gaming on mobile shouldn't be just plain bad, we the users have the last decision whether or not engage with it, some decide no, and some decide to dive in a little just to see what they can find, but just going to the official stores will not help you as the games with the dark patterns proliferate there.