I've quit mobile (phone) games almost entirely. They've ceased to interest me on any meaningful level at all, and even though I know there are good ones out there, I'm fed up with that subset of the industry and have found myself gravitating away from it regularly. But there definitely are still good things being developed for phones, you just sort of have to know where to find them.
But no, handhelds aren't dead at all. 3DS is probably still the best handheld on the market, which is why it's still being supported. It's got a fantastic library of stuff and is a solid system. It hasn't been replaced because Nintendo's next offering looks like it's going to be a portable that you can dock to use as a home console, so sort of the best of both worlds. It may behoove you to wait for that, if that's of interest you. I forget projections, but it's not supposed to be that far off at this point. But honestly, you wouldn't be bad off with a 3DS. You have the existing DS library to play with, plus 3DS games, and there are tons, many of which you could probably get somewhat cheapishly at this point. I still play GBA and DS games, so it's not like this stuff being a little old hurts the entertainment value. And 3DS games are still coming out, so many of them ARE recent even if the platform itself is on its way out.
I also still think the Vita is massively underrated. It's got a lot of great PC indie game ports and things like that, so whether it's worth anything to you is very much dependent upon what you want from it, but I think it remains a strong platform, especially because you can often get gently used ones for real cheap these days. I've been playing Darkest Dungeon on Vita, and it's a pretty fantastic port. Don't write it off just because everyone is down on it. Check into the library and see if there's stuff you want. You might be surprised.
Anyway, that's my two cents.