Making an answer out of some amplified comments, which I deleted...:
Prior to slightly-modern typewriters such as IBM's "Selectric" and some proto-computerized typewriters, mostly too expensive for individuals to buy, staff typists did not "add value" much (except for faculty who could not type), because they could not literally type special characters, which then had to be drawn in by hand by the author, by reference to the original hand-written thing. The typist would leave approximately the right amount of space to draw the characters. As you can imagine, making a boo-boo drawing characters onto an already-typed page was both all-too-easy and very annoying. In principle, one could make photocopies, but (let's say early 1970s) photocopies were much more expensive than now, and were typically much, much worse quality than a directly-typed page. (One could also type onto "mimeo masters", and draw characters on them, but this was incredibly messy, smelly, crazy. Mimeos were the closest thing to "private publication", but one could only make 30 or so copies before the "master" wore out...) The "white-out" of the time was not very good, either: it would often fall off the page.
For submission for publication, the hand-drawn Greek letters were typically to be underlined or circled in red, Fraktur with green, stuff like that.
Yes, the revise-and-retype cycle was burdensome. In effect, errors could easily be introduced by typists, and new/different errors the next time, after the author proof-read.
Since there was usually only a handful of typists per department, even the people with some seniority would have to wait a week or two or three for re-typing, adding another delay. But most people were reconciled to these delays, especially since learning to (genuinely!) "type" was not so typical in those days! That is, in high school in the U.S., people studying "business/secretarial" stuff, not planning to go to college, would learn touch-typing and shorthand. People "going to college" often did not learn to type at all, and possibly did not possess typewriters at all. For such people, there was no real choice but to give hand-written manuscripts to typists, even if the whole process was slow and crazy-making.
With the advent of the Selectric and such, and especially proto-word-processors that could treat non-Roman characters and do corrections and remember things, typists did add value, even for those who could type, because they'd have those machines, which were too expensive for typical individuals to afford. Serge Lang was an exception: prior to 1977 he had his own Selectric, and was an excellent typist (unsurprisingly). The hitch in using those things was "changing the balls", because not all characters could be available at one time. So this slowed things down quite a lot. The usual trick was to leave spaces for exotic characters, and go back and fill in by ball-swapping... which lent itself to the same annoying boo-boos as with hand-drawing characters into blank spots on a page. And not all characters were available... And any diagrams would still have to be drawn by hand.
With the advent of widely-available desktop computing either provided by math depts, or, eventually, cheap enough for individuals, again staff typists no longer added much value except for those who couldn't really typ, and the possibility of revising-without-completely-retyping changed everything. I note that pre-word-processing, seniority determined access to and priority with the limited staff typists, and wait-times for typing or retyping could be weeks. And as recently as 2005 I observed a senior colleague giving dictation to one of the few staff who could take shorthand, to type up a letter, and the person giving the dictation would make the now-almost-forgotten editorial marks on the typed copy, send it back for retyping. There was/is "status" in giving dictation or having typing done by others?
Formatting was not really possible either, except at publishers' houses. Sure, one could hand-draw, but they'd re-typeset everything, so any visual effects an author came up with were a waste of time. Perhaps the ugliness of mathematics manuscripts in those days (as in early SLN's) reinforced the quasi-Platonic mythology about the mathematics itself, since it sure didn't look so beautiful when clumsily drawn in by hand on the page!
The several years of the availability of desktop computers but without anything resembling TeX (mid 1980s) allowed much time to be wasted typing things up in file formats that were obsolete by the next year, etc. That was irritating. The desktop computers of the time had tiny memory, were literally slow, were unstable, and the daisy-wheel printers took a couple minutes to print a single page. And jammed. And...
Some faculty seemed not to mind demanding endless revisions from typing staff, but to me this was awkward, and just doing it myself was easier, since I had learned how to type. A significant number of the grad students at Princeton did type their own theses in the 1970s, but many did not. But the quality expected was really very low, so that lack of what nowadays would be minimum-allowed-quality was ignored.
All that effort expended to create even a crude document did distract from the content, yes. Cutting-and-pasting and moving things around and search-and-replace were really infeasible, not at all worth the trouble unless there'd be a major disaster otherwise. Just getting a reasonably correct thing onto the page was already a considerable accomplishment. Whatever had been more-or-less correctly typed so far was "frozen".
Thinking about it, it seems to me that there was much less self-critiquing done in those times, because it was so difficult to create an easily-readable document, typed or handwritten. That is, it was simply harder to subject one's own writing to careful scrutiny, because the typical copy would be (perhaps semi-legibly) handwritten, many cross-outs, pieces of paper taped on, white-out, ... In particular, the "notes" were much less an incarnation of mathematical ideas, I think, since they were inevitably a crappy version thereof. In contrast, nowadays it is possible to have "notes" that other human beings could read, etc. :)
Even before today's set-up, some people (including me) did try to skip the hand-writing step to the extent possible, exactly because hastily handwritten text was almost automatically not-really-readable by anyone else, and because typing prose could be much faster than hand-writing it, even with old typewriters.
A large difference seems to me to be in computations. "Long ago", of course all computations were first handwritten, and errors and revisions were a horrible mess. In contrast, nowadays one can typeset the first attempt to make it legible if not correct, and iteratively correct it, rather than repeatedly starting over, etc. This possibility, of iterative computation via typesetting, was absent in the dim past.
Also, getting other peoples' opinions was of course crazily slower: time-lag for typing-up, and then actual physical mail, further impeded by "campus mail" at both ends... in contrast to emailing a PDF. In fact, international mail ("air mail") often failed entirely... :)
So... "yes". :)