I know nothing about this except 5 minutes of googling, but seems like USCIS does process renunciations on US soil:
>Further attempts by prisoners to renounce under 1481(a)(6) continued to be stymied by a United States Citizenship and Immigration Services policy that applicants had to attend an in-person interview and demonstrate that they could leave the U.S. immediately upon approval of renunciation. [0]
Reading between the lines though, the process seems far harder than doing it aboard because you must demonstrate "intent to relinquish U.S. citizenship", meaning cutting off all US ties and establishing foreign ties, and that's hard to demonstrate when you're physically inside the US.
[0] https://en.wikipedia.org/wiki/Relinquishment_of_United_State...