Lynx came out the same time as the Game Boy, and Nintendo didn't have a monopoly of the market, just the right game at the right time.
Historically, that's what it takes. Super Mario Bros. (NES), Tetris (Game Boy 1st life), Sonic the Hedgehog (Genesis), Pokemon (Game Boy 2nd life), Final Fantasy VII (PSX), Halo (Xbox).
Truthfully, I don't see that coming out for any system. Just more of the same, with a bit of variation on the DS. I think that will be what really will make people take notice of either system.
You missed GTA 3/Vice City.
I believe DS is more than a "bit", but it´s up to the developers to profit it.
Tetris on Lynk or GG wouldn´t have been the same story. Specially for a game like Tetris you want your system work the maximum time possible, and you want your system is small enough to fit in your pocket (hardly in the case of a Game Boy, impossible for Game Gear and Lynk). You don´t need panoramic screens, analog sticks or incredible technology.
Tetris is exactly the reason I believe that in the handheld market, battery counts, a lot. Tetris or Pokemon are that type of games that you pass hours and hours without noticing it. Change 10 hours for 5 or less and you will have a lot of people pissed.
Other thing is that Sony is able to open a new market where the people don´t care about battery, but for the quality of its entertainment and the beauty of the tech. And I don´t deny Sony can do it, because I feel it that way too (I wouldn´t have a PSP preordered months ago if not). I will have DS and PSP and will enjoy them, but in different ways.
But actually, that market doesn´t exist in the videogame handheld industry. So claiming that battery has not been important in handheld looks completely wrong to me.