Hi,
I have already found similar suggestions that go in the same direction, but these were years ago.
The idea is to introduce eggs. You would get these in events and for example from bosses or other pve content.
To hatch them you would need incubators, which you can buy for ingame cash (money sink). Then you have to walk a certain distance with them. The distance can be tracked as with repel.
The whole thing wouldn't be breeding either, just a different way to get pokemon, which then have random iv again, but you could perhaps set the ability so that it's worth spending something on.
In addition, you could also bring in special "event forms" that you can then find in every 50th egg.
Hope you like my idea