Flutter does handle accessibility on the web, but not very well. You need to press a button hidden from non-screenreader users and then Flutter will make a tree

Flutter does handle accessibility on the web, but not very well. You need to press a button hidden from non-screenreader users and then Flutter will make a tree of dummy elements with aria attributes that let you use the app. You can see this if you use a screenreader or your browser of choice's accessibility tree inspector on the demo app.