You can make text selectable, but it still won’t behave at all like normal text. Selection word boundary things won’t match the local platform behaviour, touch behaviour cannot possibly work properly, things like context menus won’t work properly, and more.

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.