Consider any undercover operation - they're always pretending to be a 'pizza man' of some kind.
The rules are in place to prevent entrapment, which is the solicitation of an illegal act. Cutting off your power - while mean and objectionable, doesn't seem to be covered under entrapment.
I think cutting off the power (or network connectivity or water or whatever) without permission or lawful non-enforcement-related-purpose might itself be criminal, and could easily be argued as a form of coercion.
Well why would you invite a pizza delivery guy in without any pizza? Actually now that I think about it I don't ever recall inviting a pizza delivery guy into a dwelling as opposed to paying at the door, so that wasn't a very good example. But I thought your objection was 'not really a pizza delivery person' as opposed to 'not actually carrying pizza'. It sounds like you would be OK with it as long as you got lunch out of it :-)
I am far more okay with an agent with the skills to address the problem showing up and fixing a naturally occurring problem, than I am with an agent pretending to fix a problem they created. Of course it's easier to find an agent with the skills to address "no pizza" than "no internet". And "more okay" doesn't mean "okay" - I've not thought sufficiently deeply to confidently say which side of the line that falls on, but I'm at least a little leery of it.
The rules are in place to prevent entrapment, which is the solicitation of an illegal act. Cutting off your power - while mean and objectionable, doesn't seem to be covered under entrapment.