Background updating should be a thing. It is available on every major console. It never works. That can be fixed.
Additionally, there have been rumblings about where innovation is going to surface in the next generation of consoles. One of the more consistent themes is the handling of downloads; it'll be easier for developers to "shard out" their game into the components that, say, a particular mode or level or segment need, in order to get players into the game as quickly as possible. It may be a 50gb game, but you'll only have to download 3gb of it to get started.
We're seeing some of this on the XB1/PS4 today, but usually its very binary: Ready to Play, then Full Download. Next gen consoles will get much more specific and optimized. I believe (don't quote me on this) Sony has outright said that their goal is: you buy a game and you play it instantly, with no cloud rendering/streaming; just really smart handling of downloads and packaging.
The most ironic thing about gaming over the past generation is that games always used to be like this: you buy a disk/cartridge, and you're playing. Nowadays, you buy a disk, the disk has to install to the drive, then there's a day 1 update; its a total mess. We'll see how the next generation looks, but I doubt very much the situation will look much better for people with bad internet. If you've got great internet though, maybe we'll be close to the way it looked in the past.