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.
Flutter for web is quite rapidly improving in all the areas you mentioned. For right now I think it's already very suitable for highly complex browser applications such as a Figma, Google sheets etc. Load times aren't the best due to a quite hefty WASM download, but for _applications_ that you typically open only a couple of times per day and where you work in for several hours, that initial loading delay really doesn't matter.
Just don't expect to use it for an E-Commerce site or something like that.
Flutter web is not fit for consumer facing products imo, it renders in a canvas so the performance will never match up to html+css+js.
I've used it to make desktop apps but there's still some rough edges but it's getting better. Definitely better than electron though.
I want to try out Flutter, but my main target is Web and Desktop apps (Recent update from Flutter for Windows Desktop Apps made me want to learn it)
I have heard several criticisms regarding flutter for Web, that bundle sizes are high and load times are slow.
What is your opinion? How was the experience, and most importantly, is designing apps with flutter easier on the cognitive side?