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.
Also let me add one more details most phase converters useally are wired in delta format so that why many converters instruction warn do not hook up any single phase loads on manufactered phase due pretty much a wild leg format.
It the same idea with standard 4 wire delta format set up.
Pas de problme,il marche n'est-ce pas?"(No problem, it works doesn't it?)
If you hade a single phase load that worked with the available voltage coming off of the manufactured leg.
Imagine the 3 phase panel with every thid breaker not used because it was a manufactured leg. Somebody wants to add a single phase circuit that would only get used if the equipment using the phase converter is running. For instance task lighting or an external auxilary pump. This somebody measures the manufactured phase to earth voltage and decides that it is close enough to operate the device in question. So they drop in a breaker and away they go.
Notice I did not say that this someone was qualified to perform this installation, it is just someone who knows enough to be dangerous.
I hear what you are saying, and being dangerous they would install a breaker that was not rated for the voltage to neutral of the manufactured phase and the piece of equuipment the installed would be manufactured and listed with the voltage to neutral also allot lower than this installation would be. I think the requirement just from this standpoint is smart.
Otherwise placing single phase loads on only this line may have a major adverse effect on the manufactured phase of some equipment. Why not just require the products main listing treat all products the same and avoid the dangerous person per chance they read the installation instructions.