IMO, Flutter for web only makes sense if you already have a mobile or desktop app done, and you are looking for a quick win: if your app is architected properly, adding web support for a mobile app project is really a matter of hours (or even minutes) which is amazing if you can live with the less-than-perfect UX.
Flutter on the web looks like Flash, everything feels very off, scrolling, keyboard support, text selection, etc everything just feels strange or doesn't work and it provides a poor end user experience.
Apart from the good mobile experience, I'm also excited about Flutter on desktop. It might not be "there" yet (I don't know, I am not using it in production), but it's promising and could be a good alternative to native desktop development and Electron.