The purpose of the Late Roman Draco standard.

[Urselius]

A vexillum and a labarum were similar, but distinct. A vexillum could carry any device, but a labarum always incorporated the chi-rho monogram.

I think you miss my point slightly, the earlier assertion was that the draco somehow represented a tie between the emperor and a particular unit. As was pointed out there is no contemporary written evidence that this was the case, however, Eusebius (a contemporary writer) states that Constantine gave labara directly to the units of his army. I believe that this is the only written statement concerning the wholesale donation of standards directly by an emperor to military units in the Late Period. It therefore has priority, due to its primary source origins, over any other theory proposed for the type of standard used by emperors to tie units to themselves.