If it's not allowed to do something, I'd rather it just show me the error it got when it tried and leave it to me to tweak the containment or not. Having it refuse because it's not allowed according to its own internal logic just creates a whole separate set of less-common error messages that I'll have to search for, each of which is opaquely equivalent to one that we have decades of experience with. There is a battle-hardened interface for this sort of thing and reimplementing it internally to the LLM just isn't worth the squeeze.
I will confess that I've previously run untrusted agents (e.g. from CircleCI) as my own user without giving them due scrutiny. And shame on me for doing so. I just don't think that my negligence would be any greater had it contained an LLM.
Basically, an LLM can have the ability to access the web or it can have access to private information but it can’t have both and still be secure.