The feature seemed to have disappeared once Red and Blue came around, though.
Nitpick: Red and Blue came before Yellow.
Anyway -- and forgive me if my arguments sound a little scattered -- it's a neat feature that would've made things more convenient than finding a certain house and talking to a woman to figure out whether or not your Pokemon loves you (in GSC and RSE, at least, given the fact that those games actually have happiness-induced evolutions), but it's not really something I felt was particularly vital. It was nice, but as lettursnumbers pointed out, it was a feature put in because Yellow was based on the television show -- meaning the entire point of the game was to see what it was like to be Ash, right down to the outside-of-the-ball Pikachu. So, I really didn't think too much about it at first because I just felt all it was was wish fulfillment for the anime fans. Not that that's a bad thing, really. (That and I kinda wanted a Raichu and couldn't trade at the time, which made the Pikachu thing a little grating to me.) If we got to choose what Pokemon followed us, that would be cool. On the other hand, it would also mean hundreds of other sprites, which in turn means the game would require more room (which I don't think the earlier cartridges had).
DP tried to bring back the idea with Amity Square, but even then, there's barely anything to do in that park except walk around and wait for your Pokemon to pick up an item. On top of that, the number of Pokemon (anything that would be called "cute," which really eliminates a ton of Pokemon that could probably fit this category) just narrows the choices down. Space isn't even an issue here in this case, given the fact that a DS game card can really store a lot more information than its predecessor on the Gameboy Pocket (i.e. Yellow). Point is, if fans wanted it, it's probably possible to have a wider range of Pokemon following the trainer around.
Would
I personally want it? To tell you the truth, I'm sort of indifferent about it. It depends on what later games would've done with it, really. As I've said before, it's cute but not vital to gameplay, and when it was brought back (in a sense), it was a fairly boring feature. Personally, as I've said before, if you got to customize (not talking about having a starter follow you around because there's a lot of other Pokemon I'd like to see trailing behind me), then maybe it might be cool, but if you didn't the way you couldn't in Yellow and you pretty much couldn't in DP, then it really doesn't add anything to the games for me, even personalizing it. But that's just my view.
