I haven't really heard a lot of people thinking less of handheld systems as someone mentioned here, other than than perhaps that they don't like handhelds in the first place. I think especially the Lynx got a lot of praise in the magazines for being hi-tech.
High tech... for a handheld.
At the time, it was just assumed that you had to make compromises to fit any amount of computing power in a thing you could hold in your hand. People weren't walking around with these immensely powerful palmtop computers (aka cell phones) that we all have now; any kind of handheld computing was considered amazing just for existing. But that doesn't mean most people thought it was good in absolute terms.
So it just went unspoken that handhelds were considered lesser and secondary to home consoles. You wouldn't have read about it much because it was just common knowledge; the sky is blue, and handhelds suck. Not many people really took them seriously; they were something you whipped out to play a quick game of Tetris on the train. That's all most people ever used them for at first.
It also wasn't considered necessary for them to be any more advanced considering how well the Game Boy was selling, which was practically anachronistic the day it was released. But, yeah, it had Tetris and Mario, plus a lot of other crappier games with famous names, so people bought it as a time waster.
The Game Gear and Lynx both tried to push the technology forward, but they both had to make just as many compromises as the Game Boy did; they just made different ones. They sacrificed size, battery life and screen quality in order to get a bit more horsepower and color. But it wasn't even *that* much more computing horsepower; if you were to show people most Game Boy games vs. most Lynx games and just turned the color off, I'll bet most people wouldn't know they were from different systems. And for me and I think a lot of other people, the quality of the screen itself made it hard to enjoy the color from the Lynx, which negated a lot of that advantage. At least the Game Boy had a really sharp screen, even if it was pea green, slow, and not lit.
It would still be a long time before the compromises in handhelds became harder to notice and/or easier to ignore. But at the time, they were just glaring. And I don't think the compromises Atari made were the right ones.
*Now*, most of that doesn't matter, because it's not like the Lynx is trying to compete against the Switch. Once time has passed, we're all able to look at these things devoid of the context they once had. But the Lynx does still suffer from compromises that I feel like make it hard to enjoy even in a vacuum. I did mention the screen mod that at least takes care of that problem, and that's probably the only real dealbreaker for me at this point. I just need to finally pay the money and do it one of these days...