Google does something like this with the GMail app on iPhone— you click links and instead of just opening Safari, it pops up a "which browser to use" selector modal, which is really just an advertisement for you to install Chrome.

This is what I want personally.

I use different browsers for different things: let me fucking chose which browser to use.

I am currently wondering how easy it would be to build a "shim browser" that you can set as default but does not actually open the page, it only list the urls apps tried to open and lets you copy them to whichever browser you prefer.