One of the things I've seen in other editors is a "fallback mode" paired with clever windowing on syntax highlighting. Procedurally, the editor starts by using the fallback mode to highlight the file. Fallback modes are not allowed to have context, their regular expressions must be free of all backtracking, and everything has to be line-bounded. Basically, it's simple tokenization and nothing more (note that this will mishandle tons of common constructs, including multi-line strings).
Then the editor attempts to refine the fallback mode with the main mode, but bounding as much as possible within the active view subset of the file (plus/minus some reasonable expected scrolling). With modes that have neatly-closing contexts, this actually works out fairly well. For example, imagine the active view is in the middle of a class body, with the class starting just above the view and ending just below. The class body will pop most of the active contexts off the stack, and you'll end up with just
source.whatever. You can defer applying the full highlighting to the text above and below the view. There are clever ways to extend this to certain forms of contexts as well (e.g. situations where you don't have things neatly popped off above and below), but you get the idea.
The main thing you lose here is symbol indexing, since you can't ever fully-contextualize the entire file. I don't think that would be a surprising loss for most people, especially if it is accompanied by a warning (e.g. a banner at the top of the view, indicating that limited highlighting is in effect, with an option to turn on full highlighting at the cost of performance). You do get to keep the minimap, which is sort of fun, though it will have limited accuracy outside the current view (and for that reason, it might be better to disable it on such files).
Obviously, this is certainly a significant amount of work that may not have value, and might even (depending on implementation) require backward-compatible changes to modes to work optimally. But it does allow for opening and editing enormously large files.