I can probably add a little to the, uh, discussion. Having had some substantial experience in various aspects of processing.
First, in case this is all one reads... IF your water contains ANY hard particulate matter, DO NOT try using a squeegee. Once you get such a particle caught under the edge of a rubber squeegee there is a good possibility you will get either a scratch or at least an indentation.
Back to squeegees in general... in high volume commercial processing these are almost a necessity, in multiple places. For effluent control ("pollution") if nothing else. Additionally they can reduce total chemical waste quite a bit - this is via the efficient use of "replenished" chemicals. The way this works is, loosely, when wet film comes out of one bath and into the next it slightly dilutes that next bath. Said bath, therefore, without squeegees, needs higher replenishment rates to stay at the desired concentration, which in turn means more total chemical waste. And if one collects the excess volume of certain baths, in order to "regenerate" them, it's better that they are not overly diluted. (Note: to regenerate a "waste solution" means means to restore chemical concentrations back to aim spec so it can become a replenisher again.)
Additionally such processing occurs at a certain machine speed which means that the film must be fully dried by that time (so it can be rolled up). So there is a fine balance between the temperature and humidity in the processing machine's drying cabinet. As well as some predetermined "moisture load" in the film itself, generally based on squeegee'd film. If one does not squeegee the film there will also be droplets or runs of water in the dryer, most likely leaving differential drying marks, and in a worst case some still-wet portions of film wound up onto a roll.
So to repeat, multiple squeegees are near essential in high volume processing.
Now, my personal experience has been MAINLY with cine processors running primarily the slow-speed Kodak professional portrait/wedding films of the day. Both 70mm and 35mm film, running several miles of the latter each day. (I didn't run the processors; I was primarily a QC guy with oversight over the so-called "process control" and other aspects of film quality, working closely with both the machine operators and tech services, who performed all of the maintenance. ) I also personally designed the "effluent-control" strategies we used. So for a C-41 cine machine we used squeegees after: developer, bleach, the water bath preceeding fixer, after the first fix tank (fix-1), after fix-2, after fix-3 (I wanted to use a 4th fix stage, but the machine's frame did not have enough room; consequently I spec'd a higher replenishment rate to compensate). And finally, a "squeegee" immediately prior to the dryer; I use parentheses cuz it's not a conventional style squeegee. (I'll explain later if anyone is interested.)
So the obvious question people here might ask, how often did we get scratched film? Well, essentially close to never. As a wild guess I'd say perhaps once or twice a year we might have gotten a short run of a minor "pressure mark."
Next question, how? I'd say a handful of reasons. First is filtration of incoming water, as well as same in recirculation systems of all chemical tanks. Second skilled and motivated machine operators; they watch everything in the machine, particularly for scratches (these cine machines have open tops so can see film over the tank crossovers on the "light side"), and when it gets leadered down they scrupulously rinse down all parts above solution level and inspect squeegees. They do the same before machine start-up, etc. Next, a good squeegee design, probably unknown to most of the users here. As I recall these came out about 1980ish, called delta-something squeegees. Essentially they used molded "rubber" blades on the end of a thin fiberglass/epoxy(?) strip, perhaps 2 or 3 inches long (and as wide as the film, plus a bit). The fiberglass strips act as springs lightly pressing the "rubber" wipers together. The shape of the wipers allows splices, or whatever, to easily pass through, only rarely needing readjustment. Etc., etc. (As a note I know that at least one one photrio user has a copy of the first SPSE Handbook (1973?); this squeegee style is not in that edition, but IS in the1997 IS&T edition.) Next, these Kodak films are especially rugged in this respect; it's part of the film design. And finally, before machine start-up each morning, a nominal 20 foot "scratch test" was run (along with a control strip). This was carefully examined (for 3 or 4 minutes) by both transmitted and specular reflected light for any sign of defects. Only after this (and the control strip) were cleared would the cine machine start running production film. So one might say that management support was clearly behind these quality efforts. I should probably mention that each week all machine racks were pulled and scrubbed down by the operators.
As a sort of conclusion I'd say there are several tiers of "how finicky" (I didn't wanna say anal) one gets about processing. Ranging loosely from a casual "it's plenty good enough" hobbyist approach up to a high-quality high volume pro lab (if such even exists anymore). In the first case I'd hesitate to recommend using a squeegee. Better to get potential drying marks than possible scratches. Although it IS possible that the water is clean enough (free of hard particulate matter), and they are careful enough with the squeegee to get good results. Something of a crap shoot perhaps. On the opposite end squeegees were, at one time, virtually required. In between, use of a squeegee strips surface water, mostly preventing differential drying marks, but it may take a certain "professional" approach to avoid scratches.
I'm thinking that the person taking this so-called professional approach does things in a certain careful way that they sorta presume everyone else also does. (After all these things seem obvious, right?) But the thing is, this "professional" approach is probably the cumulative result of years of experience. They may have learned, for example, that when maintenance work is done on their hot water system that some hard water deposits (scale) may break free in the line, and some may pile up around a water filter. So when that filter is next changed some of the particulate may accidentally get past the filter seat. Ultimately maybe some slight film scratches could occur. The sorta professional approach I'm talking about would be to say, oh, I'd better flush that line out for a couple of minutes "just in case," and then change the filter and flush it a little more. But not everyone is gonna think that is an obvious thing to do.