It’s been a very common request for more and more things to run locally on the hub itself. The issue with webCoRE (and other 3rd party apps) is that they themselves run in the cloud.
The best advice so far has been to keep your critical routines in ST itself using devices and device handlers that run local. There is a list of those handlers and devices here: FAQ: CONFIRMED: Local Processing - Working Device Handlers
I’ve been trying to make as many of my devices run local (and using the SmartLighting smartapp) for my “critical” routines. So far, I have about 40% of my devices running locally.