There are several problem with that. One is that the web worker would block all user input, including scrolling, while you were modifying the DOM. Also, the locking would absolutely have to be manual. Locking before each DOM modification and then unlocking after would be disastrous, since you'd have no guarantees about the DOM's state from one call to the next. And once you introduce manual locking, you're largely defeating all of the safety guaranteed by workers in the first place.

Or think of it this way: If you can lock the DOM reliably and efficiently, then you can write code that shares memory by storing data in the DOM, rather than copying it between workers. That would get you most of what you get from ordinary threads, albeit with only one lock available. This would be such a huge convenience and performance win, that if it were possible, they'd have done it to allow memory sharing without going through the DOM at all. That right there should tell you that allowing DOM access from workers by locking is impractical.