Webrender works like the rendering logic of a game engine. The input-handling logic of SDL and friends are badly impoverished compared to what full-blown GUI toolkits support; input methods, accessibility, multiple windows, tooltips, modal dialogs, etc. are all things the GUI toolkit takes care of.

It would be easier to simply build a Qt version of the bits that depend on GTK, so Linux users can choose between those two. But considering how little Firefox seems to care about Linux user experience (FF has been broken with transparent GTK themes since forever and nobody cares; FF removed Linux native audio support and nobody cares), I doubt this will happen and I doubt a patch would be accepted upstream for reasons of "maintenance overhead". This ignores that maintenance overhead is much higher when two independent parties have to maintain the upstream and a patchset, but is for some reason accepted practice in the open-source world.