I mean, I understand many games give us the choice of first choosing the assets quality and just then start downloading the patches to increase resolution and textures 

But from my experience those are the minority. I actually don't have a good TV, 1080P is the best I can go, so no reason to me expending local storage and consume time downloading 4K assets I can't really make use of 

I wish we could have more controls over this issue 

There is no extra data to increase resolution, and even the so called '4K assets' are still not all that sharp when you get up close at 1080p. RAM is the limiting factor, hence you have those so called '4K assets' for Xbox One X. That's a limiting factor of the hardware, not the output. They could add options to leave different languages out, sound takes up a lot of space.

However for all these 'new' 120 fps modes, you could leave out a lot of data since those modes don't only need lower output res, but also lower res textures and other assets to keep up.

I think it's a false assumption to assume that downloading "4k assets" won't bring any benefits to a 1080P user.
There were 7th gen games which had 4k or higher resolution textures despite the fact that games often sat around the 720P resolution mark.

Even 4k resolution games downsamples to 1080P, which provides a very clean and crisp image on a 1080P panel as it's essentially a very expensive form of "anti-aliasing".

So yes, even at 720P/1080P you do want higher quality assets... Because we aren't at a point where games look photo realistic even at 720P.

If storage becomes an issue... I am of the mindset of just expanding my storage.

Or if you want to save money erase games you aren't going to play. For me there is enough space on the console for like 5-10 install at once and it is sufficient.

For the most part probably not, but they most certainly could. That said, I think games use e.g. different models at different distances (you don't need as many details for distant objects), but I don't think models take up enough space to warrant using different models for different graphical settings. But for e.g. textures I don't see why there couldn't be different assets for different settings. It's more about whether you'd want it (see Pemalite's post).

There's actually already a good video on why we have such a big problem with bloated games. And as far as I can tell, the issue isn't really the quality of assets (which actually is an important thing to want to sacrifice anyways). 

Xbox mentioned doing something like this a couple of years ago. Not downloading textures, modes, etc. I don't know if it was ever implemented, though. I just know that (as an owner of Xbox One S and Xbox One X), the X version of games was often much bigger. They just downloaded the right version automatically. 

Just for the sake of clarity, I often download the exact same game to multiple consoles.

Exactly, but you can't get that into people's head. 

I remember when Rage came out with with it's 32k textures and people went: "Game has low res textures. It looks so bad when I get close to it". That wasn't the point of implementing it. It was to have unique textures across the surfaces and they did a great job with it. The places you visit have all a unique look to them.  

No surprise, Dreamcast had HD texture packs.

Thanks everyone for the explanations  this was a very good thread for me