In addition to the pitfalls mentioned like being unable to select text, every interaction including scrolling is noticeably laggy and dropping frames.
Because of this alone I would not use.
Additionally, see: https://news.ycombinator.com/item?id=43215065
The only way you can get the proper behaviour for these things on the web is to use actual DOM text. Some parts of it could in theory be made possible, but I doubt that anything meaningful will ever change—it’s too antithetical to the nature of the web.
Indeed, Flutter will never do everything "properly". But that's not its selling point. It doesn't need to, as long as the number of users reached from a multi-platform release outweighs the users lost because they were offended by a missing native feature. (Assuming you're not some massive company developing a parallel app for each platform)