I just find you people who are determined to hate on the amiibos to be so silly. In just about every game I can think of, amiibo provide some minor little addition to the game that, often, I don't even bother using. The only game i've really seen them implemented heavily into is Super Smash Bros, and that was certainly a complete game without them anyway.
They definitely have a "DLC" aspect to them, but they're rather different in some ways as well. Mainly, you get a fun little figurine to go along with it, and it can be used across many games as opposed to just one. Otherwise, for most games you'd never even realize you were missing out on anything and, after seeing what it does, might not even haven my interest in whatever it adds.
They certainly walk a fine line between the amiibo being pointless and they being too useful to the point that it's necessary day 1 dlc, but I think theyve done it well so far. What I'd like to see them do, though, is come up with abother game or two (preferably ones that are actually good) that is specifically designed for amiibo (and make no claims otherwise) so that they have some serious use in games intended for them while just bringing a little extra flavor to the other games. Can't say I've liked the games they've released targeting the amiibo so far.
Otherwise, the existence of amiibo has not affected the experience for people without them in nearly all of theirs games so far... There's no need to hate them, just don't get them.