To be fair, they do have mandatory requirements to prevent their employees from doing some things online in some cases. For example - some of the rules around coordination on a trading floor: https://www.sec.gov/rules/sro/nyse/2017/34-80374-ex5.pdf
Or - in many cases they are legally required to retain a copy of communications sent, and there are a large number of sites that offer diverse services banks want that also happen to have "chat/email" hidden as a feature. That's legally communication, and they often can't collect and retain it.
Long story short - they don't really care so much, because many of them are already doing this collection now in other ways... my first job out of college 13 years ago was helping large banks transition this monitoring and policy enforcement to browser extensions (Guess who was grumbling about the MV3 changes in chrome, for very similar reasons).
Now they're moving to directly adding the monitoring in the OS/Kernel