Flutter is a cross-paltform app framework. If you have a app on all platforms you (the company) care about the web app would often become just a seconds class citizen which you (the company) only have as some users are hesitant to install apps and some few users have some exotic platform or need access during holidays after their laptop was stolen etc. Anyway from a business POV a second/third class citizen you don't want to spend much money on. So flutter web would be good enough (once it's out of beta, at which point text selection likely will somewhat work).
But if you ever have a web app as first class target you probably would never go for flutter anyway.
My prediction:
- Flutter will long term be come the new default native way to write apps on google phones. Dart will very slowly replace java.
- Flutter will become a serious way to write the UI of apps on Linux, through maybe not as big as Qt/Gtk. But likely a common choice companies which target Linux as 2nd/3rd class citizen.
- Companies mainly targeting Android will use flutter for their iOs, Windows, Linux, Web apps to save cost.
- Google pushes some new Web API's around accessibility to provide a better flutter on web experience. Making it again harder for non chrome browsers, through in this case not intentionally.