There has been 1 game I've tried to play that hasn't worked, people say it does, but there are 2 versions of the game (square enix, final fantasy 8) and I have the older version, for some reason no control input is sent to it no matter what I do. I'm sure if I bought the new version it would work fine, but I'm done with that company after they bricked my phone copy of ff6 (even though the phone didn't change at all) and told me "if I want to continue playing you need to buy the new version". I'm sad they seem to be doing the same thing with all their old games.
That rant out of the way.
I have 1400 games in my steam library, the above is the only one I've wanted to play but haven't been able to get working.
I highly suggest a Bluetooth mouse and keyboard for first person style games (I'm too old to get used to the "gyro control fine aiming", but the younger people say it works great.) and 4x games.
I play a lot more 2d platformers and rogue-lite games on the deck than I ever did on a PC/laptop. The controls are fantastic and there's no input lag like I used to have with a wireless control to my PC.
I'm about to buy a 3rd because my household, and the company we bring over, sometimes use mine when I want to be using it.
Some of the games I've played on it: red dead redemption 2, Witcher 3, elder scrolls Skyrim, rim world, dead cells, path of exile, Warhammer total war 2, sid Meier's civ 5 and 6, subnautica, factorio, satisfactory, monster Hunter frostborn wrath, baldurs gate 3.
It's actually amazingly good at running the ported PS2/4 and xbox360 games, I was amazed to see 5-6 hours predicted battery life while playing dynasty warriors 8 and Disgaea 4.
I was thinking about getting a new gaming laptop to replace my 5 year old 15" dell, but the deck filled that need perfectly, and at a fraction of the price a new computer would've cost.
When I originally bought it (pre ordered the 512 gig) I bought a "leather skin" and screen protector, I'm glad that I did, but I think the skin was going overboard.
If you aren't a gamer I'm not very sure how much desktop function there is, I've only done it once or twice, but I was able to YouTube and Amazon through the browser.
If you get one (and I highly recommend it) I suggest getting a kick stand, a Bluetooth mouse and a Bluetooth keyboard.
My next investment is going to be a "dock" and a pair of a.r. glasses so I can charge it and use the glasses as a monitor and lay in bed and game until mold grows over me.
Edit to add: I've actually found a couple newer games that developers have decided my laptop is "too out of date" to run, but will run just fine on the deck, so there's that!
Please feel free to ask my any specific questions, I will answer them as unbiasedly as possible.
I jumped on ordering mine working 30 minutes of its announcement, I waited 7 months to get it, and I've used it probably 60% of the days since I've had it. I still use the laptop some times (especially when my wife has it for some games, and I bought my mom one of her own so she wouldn't be using mine constantly when she came to visit)
The weird part of this post is I've spent a couple of days trying to get Disgaea 4 to work on my Deck and it really, really doesn't. I know I'm not alone because the game's forums have several threads of people complaining about it.
Slightly embarassingly, I also tested it on a Windows ARM device and it ran fine.
Look, compatibility on the Deck is... good for what it is, but it's certainly nowhere near universal. Especially if you have a big library of games outside Steam, which I do. I'd still say it's the easy go-to for a casual gamer mostly interested in older single player stuff or indie games, particularly for the price.
My library is plenty large enough and it's 80%+ gold verified on protondb, and I've found success in running titles that were unverified (but not borked, I've never tried any of the dozen or so borked games in my library).
Disgaea 4 runs flawlessly without any modification on my deck, it does take a moment to start, I believe that is when it's trying to connect to the online servers which I have entirely disabled through the in game options menu.
I won't attest to anything outside of steam, because I didn't buy a laptop or a console, I bought a steam deck. And I have more than a thousand games ready to go on it.
Edit to add: not sure where you pulled "universal compatability" from, I never mentioned that at all. Contrary to that statement all of the games I mentioned, and everything I've ever tried playing, are titles activated through steam.
I mean, I pulled it from reality. I'm just assessing the way it works for the OP, not representing what you said.
As for Disgaea 4, I do believe that it works for you, the threads on the Steam forums also include people who say it runs for them, along with several who can get it to run by fiddling with Proton versions or doing some combination of launch options, multiple retries and settings changes. But it does have problems. It won't run at all for me and others report frequent crashes, endless loading screens and other issues. It should definitely not have a Verified rating.
That's the exception, not the rule, I just mentioned it because you pointed it out and it happens to be one of the games that don't run universally for everybody.