They will bring them back, but in an updated way (possible alliance tiers). Just wait!
Not having alliances hasn't really affected my games at all.
I think a lot of players (especially lower ranking players) don't really understand or care about alliances. It used to happen to me all the time that I'd make an ally only to see them to build up troops on our common borders and sometimes attack me, even when it was a clear that an alliance would be advantageous for both of us and that I wasn't threatening them.
I agree that knowing when and with whom to make alliances and when to break them is a critical part of Risk. But in my opinion being able to actually ask for an alliance isn't necessary. Actions speak louder than words and that was just as true before as it is now. Knowing who the useful allies are has always been about what they do, and not having the "request alliance" button hasn't changed that. With that said, I'm not against having in game alliances but I don't see them as crucial.
As far as I'm aware, removing alliances from the game is only temporary and SMG will be bringing them back in an updated form.