I am also wondering about this. Having recently built a production app in Flutter Web used by millions of people, I am very eager to hear about other people's experiences with Flutter Web in real life applications.
I've been coding Flutter mobile apps for a couple of years, but have only toyed around with the web target. In my experience it seemed kinda off. Scrolling lists ignored my native scroll speed and janked, text manipulation felt laggy, etc. It reminded me of the good old horrible days when Flash-based websites was widespread. I tested it right after the 2.0 release, so perhaps they've fixed it since.
EDIT: Also IIRC the bundle size of a release bundle was like 3mb which was a big yikes.
Yeah that was our primary risk - the actual main.dart.js file becoming too large. We host the JS asset on Cloudfront and the web app from somewhere else, which makes it much better. As far as Flutter Web itself, I only think it became production ready for the web in the last 3 months - literally! It was a bit of a risky choice, but it worked out well for us.