The easy answer is that it would be a code violation. See article 455.
For the few rotary converters I've dealt with, the manufactured phase always had a higher voltage. This could be a real problem, especially for a 120 volt load.
The real reason is probably because there is no direct electrical connection between the manufactured phase & the single phase input as pointed out in the definitions 455.2
Anymore, if I'm going to run a 3 phase motor on single phase, I purchase a variable frequency drive. If you ever decide to do this, consult with the manufacturer for the correct size. Price wise, I recently had a quote for a 3/4 hp drive, single phase input to 3 phase output, it was less than $300.
Few things are harder to put up with than the annoyance of a good example.