They've already done that. They're called the Facebook and Messenger native apps for Android and iOS. Conveniently, the Facebook mobile web app shows you Messenger notifications but won't let you read them without installing the native Messenger app, or visiting the Facebook on a desktop browser, despite the fact that direct messages have a much simpler interface than the rest of Facebook and that it used to be possible to view messages in the mobile web app, so they push for native app usage pretty hard already.

I'm not sure they'd see desktop browser warnings as much of an existential threat considering 94% of their advertising revenue comes from mobile [1].

[1] https://s21.q4cdn.com/399680738/files/doc_financials/2019/Q2...