One mislabeled film could ruin an entire process batch in a dunk dip processor.
I don't really feel like bothering my Fuji contacts with a reality-check on the above statement, but I'm a bit skeptical of its accuracy.
This is only tangentially related, but I discussed remjet with one of the chemists working at a major Fuji-run processing lab responsible for the maintenance of their chemistry (C41, B&W and a massive amount of RA4, and previously also E6). I saw some leaflets with instructions not to run remjet through their continuous processing and dip & dunk lines. So I inquired how bad it really is. He basically shrugged and told me it's actually not a major concern if it's just a couple of rolls once in a while, because all the muck gets filtered out in the inline filters anyway. Of course, they don't want things to get out of hand, so as a matter of principle, they try not to run any remjet-backed film through their C41 lines, but it's not a big priority for them to prevent it. Insofar as they are concerned about it, it's only about the remjet much and not the chemical nature of remjet-backed color film, which of course is more akin to E6 than to C41.
Of course, actual cross processing of E6 slide film is a bit of a different story since E6 film will affect the chemistry (especially the developer) in a way that filters won't compensate for and the load on the system of one roll of e.g. Ektachrome will be much bigger than a single roll of e.g. Vision3 due to the higher densities involved. Still, given the multi-gallon volume of a typical commercial bath, the odd cross-processed roll here and there wouldn't make that much of a difference. It'll add a little to the normal drift that's compensated in a well-run lab by means of control strip processing and adjustments to the chemistry. This particular Fuji lab of course does these things.
There were no signs of them not accepting hand-rolled film or being concerned about it. It's rare to begin with, especially in color, and if it happens, the impact is really minimal unless a large percentage of people start hand-rolling AND mislabeling their color film. Given the (un)availability of bulk color film, I don't they lose much sleep over this issue.
I can imagine that back in the days when volumes were bigger and more people specifically requested cross-processing, they would run the x-process rolls at the end of the day so that any drift in the chemistry would be caught by the next day's pre-production chemistry maintenance. But that seems to me more a matter of sensibility/best practice than of sheer necessity. Indeed, I vaguely recall this being done by the local lab I sometimes would bring my E6 film to for cross-processing in C41; I think they would run my film at the end of the day through their minilab so any effects it had on the chemistry would be reduced to the point of insignificance by the next morning's replenishment and control strip routine.
I can imagine something along the lines of a "no hand-rolled film" policy for very small labs who work with small and inherently less stable volumes; i.e. minilab scale, and much more limited resources in maintaining their chemistry. They might not want to risk anything mostly out of conservatism. You don't want to waste time and chemistry troubleshooting a problem without the means to actually do so.
More on-topic: I'd welcome a color bulk roll option of decent quality; let's say Gold/Superia-level. Given Harman's responsiveness to end user requests, it seems far more likely they'll entertain the thought than Kodak.