Well hold up there now. The binary that there weren't much of series until the mid-1960's when publishers decided to change things to series isn't really a workable picture historically, especially in the category SFF market and the pulps that firmly established itself after WWII. That category market was, on the book end, primarily a mass market paperback market. As you know, MMPB relies on generating lots of cheap titles sold and distributed in bulk and as such series were often useful.
It is true that science fiction authors tended to favor "standalone" novels but that word is deceptive. Category market science fiction writers tended to write series in shorter works of fiction, published in the major magazines, and they would gather those shorter works of a series together into an episodic "standalone" novel. Or they'd do a particular short story or novella that played well and lengthen it to a short novel for book form. So what looked like "standalones" often were parts of series, just series that relied on collections of short fiction with some books, or were series of short novels that had first been printed in Astounding and such. (And that's a tactic also enjoyed today with authors doing short stories and novellas in the same series universe as their novels, including their standalone novels.) Some science fiction authors also liked to essentially have series that weren't called series because they'd take one character from one novel and put them into another. You'd have two "standalone" novels that were in the same universe, or sometimes in the same multiverse. (And this could also happen in fantasy/horror -- see Michael Moorcock and Stephen King a bit later on.)
But novel series, especially short duologies and trilogies, were not uncommon in science fiction pre-mid-sixties. E.E. Smith's Lensmen and Skylark series, Poul Anderson's Psychotechnic League series, Andre Norton's Time Traders and Solar Queen series, James Blish's Cities in Flight series, Hal Clement's Mesklinite trilogy, Clarke's Space Trilogy, Campbell's Black Star trilogy, Leigh Brackett's space opera duology, Murray Leinster's Med Service series, Lester del Rey's Moon trilogy, etc. are examples of "Golden Age" series. Heinlein himself had his first successes with his Future History series well before the mid-sixties. And serial characters like Buck Rogers and John Carter of Mars along with hundreds of imitators filled novels, short fiction in magazines and comic strips.
And again, authors are like cats. While publishers did help shape what came out when from business needs and printing and distribution changes, it was mostly a matter of what authors wanted to try out and brought to publishers (and magazines.) The fact that Asimov's Foundation series -- a mix of short works, bundled together into episodic "novels" plus then later full novels -- worked well for him, as did his I, Robot series of shorts, meant that a lot of would-be SF writers tried to do similar things coming into the market and looked at series and serial characters. As getting work into the magazines slowly did become less important in the late sixties onward to a greater emphasis on doing novels instead (which was the result of more SFF publishers forming and putting out more titles, again mostly mmpb, more bookstores and changes in the magazine market) authors didn't really need publishers to tell them that book series were potentially lucrative. Many of them simply switched from doing series through serial short stories and novellas to doing more book series. Concentrating on books from the beginning instead of starting with initial shorter work also meant that authors started writing longer science fiction novels as standalones or series, playing with the form.
Fantasy changed from a short story centered marketplace to a book one even faster than science fiction. Many fantasy stories need more back story and world-building than science fiction stories, so the longer form was a natural one that drew fantasy authors' interest. They also grew up with more fantasy novels and series through children's publishing and fiction that was often offered to children and teens even if not originally written for them as the audience. Carol Kendall's Minnipins series, E. Nesbitt's series, Baum's Oz series, Edward Eager's Magic series, The Borrowers series, Lewis Carroll's Alice in Wonderland stories and of course C.S. Lewis' Narnia series -- all pre-mid-sixties -- were the type of works that fantasy authors were weaned on and influenced by. Fantasy authors were also influenced by category fantasy serial characters like Conan the Barbarian and Jirel of Joiry and series such as Jack Vance's Dying Earth, Mervyn Peake's Gormenghast series, Ray Bradbury's Green Town horror duology, H. P. Lovecraft's series, L. Sprague de Camp and Fletcher Pratt's Harold Shea series and things like T.H. White's Once and Future King, which is several novellas bundled into one book, etc.
And as we already established earlier in the thread, fantasy authors were doing lots of trilogies in the category market even before LOTR became mega-popular as a large novel split into three -- it was simply a popular form. And again seeing the success of LOTR and other trilogies meant that many incoming fantasy authors who wanted to do a portal/multiverse or secondary world fantasy story decided to play with the same form of series as LOTR. No one had to tell fantasy authors to do series -- they were well experienced with the whole idea. And again, doing complex stories in shorter volumes could increase a chance of a deal with publishers sometimes more than one large book (at least till publishers got pretty quickly that fantasy readers adored large books.) Some fantasy writers who were doing more urban fantasy or things like supernatural mysteries wanted to do episodic long series like the non-fantasy mystery writers did and when some of those started doing very well, more fantasy authors who wanted to do stories like that tried that form.
Horror was the one area where standalones remained the favorite form for authors. Which wasn't to say that they didn't have series (Lovecraft) or come up with them in later years, especially short series. But trilogies and series, with or without publishers' interest in them, aren't as favored by authors doing horror where maintaining scares is the goal. They do sometimes like to do duologies. The slasher film series since the 1970's have influenced some series in horror and there's been spillover into dark fantasy series, but overall it's just not as much of an interest to the horror writers.
Basically, most of the time, authors aren't listening to publishers. Instead, they are more likely, especially early on, to watch what other authors are doing, particularly if it does well in the marketplace, and then, liking that stuff, decide to play around with their own version of it. If your favorite is a quartet series, it's not a big surprise if you come up with a quartet series idea. If you are used to trilogies, like trilogies, then you are also likely to think up stories in trilogy form. But also sometimes they write one thing and it then ends up becoming something else.
For instance, if you look at your own work, Matthew, you have multiple different series that mix books, novellas/short novels and short stories that are all part of the same Archonate universe (and so technically one big old series.) Was that planned? You had multiple different publishers, book and magazine on them. They may have directed you occasionally, but I doubt they were the engineers because if they were, they'd have made you do it in a much more tidy, plate-spinning direct line. A God in Chains is a "standalone" novel, but one that takes place in the same universe as your Baldemar and Raffalon short story series. Planned, just sort of developed? Please explain the genesis of Luff Imbry.
It's not that publishers don't request things or affect things. They're the ones investing in and putting out many of these works after all. But it just really doesn't work with fiction authors, particularly in SFF, to say that the book publishers are the ones driving the bus on series or what form those series take. Even authors who are very market oriented, organized and occasionally do tie-in fiction for movies have meandering writer brains one way or another. And every writer has more ideas for projects than they know what to do with.