I've started to see boxes of water. They look like milk cartons.

Those are not at all better. They're mixed materials. Much harder to "recycle," in practice even if collected, usually just burned.

Problem is, it's not paper.

It's called [Tetra pack][1], and contains both paper, plastic and metal. Physical separation is virtually impossible (at scale), chemical separation is very environment-unfriendly.

Unfortunately in Switzerland it is dumped to trash; in Easter-Europe it is collected for separation though.

[1]: https://en.wikipedia.org/wiki/Tetra_Pak