Like I said, they're usually not as flexible (like the aforementioned not having pan knobs or 1/4" jacks for stereo channels), and make compromises to squeeze everything into that form factor and into the target budget (yet they still cost hundreds and hundreds of dollars new).
Any time I've bothered looking at what's out there on the market (new or used), I've found them completely uninspiring. It always seems like you're running into input limits, or power limits, or routing limits, etc... All the inputs are on the front which is right where they DONT belong. If you have consistent needs that can be met by a particular model, then the convenience of an "all in one" might work for you. But they usually cost more (certainly for what you get) than the equivalent in either passive mixer/power amp/passive speakers, or passive mixer/powered speakers. You usually lose like 1/3 of the mixer functions even if input channels and power output are close to the same.
But that's coming from an independent sound engineer, so my needs and perspectives and preferences might be different than yours. But for me, if I have a gig where I just need to get 3 vocals in the mains, I like to be able to use my little $90 Yamaha mixer that weighs 6 pounds, bring the amp and the mains that are the same no matter what (unless it's a REALLY small gig, then I can bring my small speakers to use as mains), and be done with it. Then if I have a gig where the band wants to mic the guitars, and they have 3 singers, and bass in the mains, stereo keys, and mic the kick and snare, I can get a hold of a 16+ channel mixer somehow, and everything else stays the same. I don't have to come up with a completely different rig for that, I just add/replace what I need to.
Just look at this...
Yamaha MG16XU
Compared to this...
Yamaha EMX512SC
You lose 2 mic channels, 2 stereo channels (the useless RCA ones don't count, what do you actually have that has RCA outs?), parametric mids (kinda important for live sound, esp vocals to get a full rich sound minus feedback), 2 aux sends you can actually use as aux sends and not just s monitor send (which you need to kill your stereocapability for anyway), sub groups, etc... And all you get in return for the $90 extra you pay is an amp that's not that powerful anyway unless you run it at 4ohms a side. And by estimate when you factor in all the stuff they leave out of the mixer, they're charging you about $350 for that. For $300, you could get a brand new GX3 that puts out 425 at 4 instead of 500 at 4 (or is that peak power on the yamaha? who knows?).
So that's why I'm not really in favor of them.