Yes, it's been considered and I've also compiled Tiled against Qt for WebAssembly and ran it in my browser. However, it will be very hard to turn it into a usable editor when running in that environment.
The main problem is the lack of direct file access. Qt provides functions to read/write single user-selected files, but Tiled generally wants to open a lot of other files, like the referenced tileset or image files. Or JS extensions, when opening a project. I'm not sure if in the meantime it would be possible to grant access to an entire folder, which would mostly resolve this issue.
Alternatively to Tiled in the browser accessing a local folder would of course be to enable accessing files on Dropbox or other services, though that will require a lot of custom integration code.
A more minor issue, but one that would take a lot of effort to improve, is that the UI isn't generally very suitable for running in a browser. On many occasions it wants to open popup windows and I'm not sure how well the dock widgets in its main window would be supported. Switching to a QtQuick based interface would be a possible solution to this problem, and would also make map rendering a lot faster by using the hardware, but it will be a major project.
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