I did a simple test, and I put in a block on my firewall to anything going to port 8883 from my Hubitat. This blocks access to the Hubitat servers from what I see.
I noticed, IFTTT broke. However, Ecobee continue to work, but if you need to reauthenticate it requires the cloud.
So the question is, does every single internet service require the hubitat cloud to work?
I don't think so. When I wrote my Pushover integration for Hubitat, it communicates directly with the Pushover servers. The Hubitat Cloud server is not required. This works because the traffic always originates from the Hubitat Hub to the Pushover cloud servers.
If an integration requires unsolicited input from a cloud service, then it needs to go through the Hubitat cloud server via an OAuth2 app running on the Hub. IFTTT would be a good example of this.