I understand that DA caches can grow very large with the searches you do.
That said, is there a way to limit the size of the cache, so you can mitigate the issues with long shutdown times, if you have the “Empty Cache on quit” option enabled?
Not yet. The only possibility is to disable the “Cache downloaded pages” option. As long as you’re not doing the same or similar searches quite often, this should have almost no impact on the performance.
Does “not yet” mean that it is planned for a future release? Is that something you plan to incorporate?
If not, please consider this my official enhancement request. 
It would be nice on storage, not to mention, quicker to shutdown if users had the ability to limit cache size.
The DEVONthink software is excellent. Please keep up the good work!
It’s at least an option for future releases. However, for most people it’s probably better to disable caching completely as long as you’re not performing same/similar searches quite often.