How about we turn that around, and have a way to enable such a system instead.

Achievements aren't a feature, they're a gimmick. They also force developers to have to make crappy game design objectives in order to accomodate them.

Improved UI, absolutely. Perhaps later on some sort of custom soundtrack support. Steaming apps would be great for those that only own the a switch out of the home console and don't already have a smart tv or some other source for steaming services. Streaming apps aren't that necessary, though. If you really want that stuff there's pretty cheap HDMI dongles out there like Chromecast.

Every else mentioned, the system really doesn't need. It's not gonna browse the internet better than a modern smartphone so why bother? Also, isn't all the social crap already going to be handled by a phone app later on? I think it's a smart move on nintendo's part to keep that stuff on phones.

EDIT: I forgot about cloud storage for saves. That one is always welcomed.

I worry about UI bulking. It might be that Wii U really soured me on robust UIs due to all of the added load-times.

I like simple and sleek, but doing it like the 3DS or original Wii would be great too. Currently, it's fine due to to most people having 10 or fewer games/demos. When it gets into the 50+ apps/games range, it could get problematic.

No, developers are free to choose how they use achievements/trophies.

Many developers just use them for tracking how many players have reached certain areas, levels, chapters, bodycounts... these kind of achievements may be boring for the players, but can contain valuable informations for the developers for future games (which weapons/races/classes are popular or unpopular, which decisions were made in majority...)

When a console has too many extra features it reminds me of The Homer. 

"I want a horn here, here, and here. You can never find a horn when you're mad." - Homer J. Simpson

That's a rather odd way to feel. You'd rather they not be there because you personally don't like them? How could them being there detract from your experience? The only thing it does is add to the experience of those that might want to use them, it doesn't remove anything if you don't want want to use them.

It's like saying "I'd rather it doesn't get [insert game here] because I don't like it."

Yeah, it could add more objectives for you to work towards and keeps you playing longer, but sometimes it just feels like busy work, feeling more to complete out of obligation rather than enjoyment. I'd rather not have a reminder of what I need to do, rather than what I'd like to do. I've found it more enjoyable to do things because I want to, not because a game tells me what I need to do. That's happened to me with a number of games, because it has objectives I'd rather not have to be reminded to do.

And there's also been the other side of "I don't want to play [insert game here] because it doesn't have what I like in it."

You aren't obligated to get achievements though. You are free to ignore them if you don't like them, and at least on PS4, you can turn off notifications for trophies, so you don't have to deal with them at all if you don't like it (in fact, I have disabled trophy notifications on PS4). It's an optional system, so why would you prefer the system doesn't have it?

Yes, I get that I can just ignore them, but why can't the people who like them just play the game without them? Do they really need them to enjoy the games they're playing?