A formal way to write the last frame's text would be "It is when one is trying to diet!" This would be terribly stiff and unnatural in AmE, though, and not at all suitable to the context.
I'm with you. One very rarely hears the subject pronoun "one" in spoken American English. It's rare in the written language as well. Some people may use it, and it would be understood, but it certainly wouldn't look natural in the comic strip OP posted.
I use 'one' a lot in writing, especially academic. I use it here a lot too. But I'm atypical in this (for AusE).
I can't see Mrs Thornapple using it. But if she was drawn as more posh, it could work.
One is pretty stiff in BrE too nowadays. I don't use it, though I do use some things that are regarded as stiff, but accept that I am going against the grain. Outside older members of the royal family, crusty journalists making a point, and academia, I rarely come across one.