In a way, you have already answered part of your own question on permission - your Execs say it isn't permitted, so unless you can persuade them otherwise, it isn't permitted.
Enforcement is something else. Perhaps the most extreme example I've come across was a client who operated a thin(ish) client / server architecture. Nothing was stored on the local workstation, all on the file server. And they enforced it by re-imaging the workstations on a rolling monthly basis. A bit Draconian for most companies, I think!
It's a difficult decision, depends on the individual, some people work best in absolute silence, whereas others can't get going in less than 80 db! Personally, provided there is no disturbance to others, I can't see the problem. MP3 players are cheap these days - that's a possible alternative if you really want to keep your PCs "clean".