2024-1-13: In Product Plan - ENH-000172764
EDIT:
Following the AGOL outage last week and Esri rebooting a few things, this behaviour seems to be much less of an issue. If you still experience it please add your kudos but also a context comment so the Esri staff have a bit more information to go by to prevent it from happening again.
EDIT 2:
Nope. Must've been a temporary reprieve as it is back to do at least 4 checks when you paste a value into an attribute table; amongst other things.
Pro 3.3.2 seems to do a LOT of license checking.
When you open the Diagnostic Monitor you will see that for almost everything you do, Pro will do multiple successive license checks.
Paste a value into an attribute table of a locally saved FC in a local FGDB: 4 checks
Rename a map: 76 checks
The log will be filled with:
<HTTPRequest start="5/11/2024 10:20:05 AM" duration="235" thread="39940" status ="200" url="https://www.arcgis.com/sharing/rest/portals/MYAGOLACC/subscriptionInfo?token=THETOKEN&f=json"</HTTPRequest>
I understand the need to monetise and audit users but how about doing this during an idle moment/startup and reporting a timestamp so you do it once a day?
Rename a map:

+ (had to scroll to copy them all)

That is 19 seconds of unresponsive UI.