So... after all of this happy conflagration and side tracking, have we reached a consensus that we CAN indeed estimate the Single Phase input current of a VFD that is powering a Three Phase motor? I think so.
I think, after reading all of this and not being swayed by the "it's not something you can generalize" arguments, that the original premise, the 1.732 ratio, is in fact incorrect, not just for sizing the VFD as I had postulated, but also for estimating the input current. It is in fact going to be close enough to 2.0 for me to say that this is the number that should be used by electricians when sizing OCPDs and conductors if the ACTUAL data from the VFD mfr is not available. I can back this up empirically as well, by virtue of having looked up several well known brands of VFDs with readily available technical data sheets that do in fact confirm this relationship (for the most part, as I said, close enough) in their published material. The "1.732" number is indeed thrown around very loosely in websites, but I see that as a "layman's term" that I believe, from the evidence, it is simply because of the relationship factor of single phase to 3 phase, so many people leave it at that, not understanding that it is wrong on all accounts. But as has been pointed out here it is not that simple because of the complexities of the way the rectifier functions. I now accept that we cannot make assumptions about what the INPUT power factor will be when feeding a VFD with single phase power (something I had not properly contemplated prior to this exercise), and that has a direct effect on the input current.
So circling back to the myth, if you look at a 2HP single phase motor and a 2HP 3 phase identical motor, the current for those motors would differ by a factor of 1.732, but that relationship cannot be applied to the difference in input current to a VFD. In my humble opinion, I therefore believe it MORE correct to assume the ratio is 2:1, and let us all lay the 1.732 thing to rest as "accurate in a way that doesn't apply to this PARTICULAR set of circumstances".