Hi, I'm pretty sure that C-41 "blix" (as opposed to separate bleach and fix) would not hold up in a commercial film-processing operation.
Where I worked we ran a couple, or so, of cine processors at, say, 50 ft/min. Film goes from developer directly into the bleach, passing through a squeegee along the way. In order to keep the bleaching step active enough we had to continuously aerate the bleach in-tank. There was a continuous layer of "pea-sized" bubbles on top of the bleach tank. (This is as described in the Kodak Z-131 process manual.) I vaguely recall a couple of times when the air supply was accidentally interrupted, and the effect was obvious on the process control charts. (Steps were taken to prevent future occurrences.)
If that step had been a combined bleach and fix (blix) I'm next to certain that the fixer portion, thiosulfate, would soon be wiped out by the aeration.
On the other hand we did successfully run PAPER processors using paper blix with no problem. The paper has a much lower "bleaching demand" such that, long story short, there is little to no problem
FWIW, regarding FILM blix, there are reasons why it's not suitable for being regenerated, meaning that the lab takes an economic hit (compared to labs that DO regenerate their film bleach.).