DO schools were the backdoor way to becoming a physician (after failing to enter into a MD school; most of them qualified to enter MD schools in the first place); they touted a pathway to PCP/preventative/holistic care. They sold the OMT idea to students. Its just an idea. However, when they started opening more schools than were DO residency spots, they were forced to seek LCME/AMA/ACGME validation of their medical school training/residency programs (by letting them take USMLEs and obtaining ACGME accreditation).
The DO degree was not established as a "backdoor", it was established as an alternative form of medicine along with the other alternative types that started around the same time. It wasn't until WW2 that DOs really started getting more traction as far of practice rights due to their involvement in military medicine. There was a time when DOs only trained at DO residencies and there were sufficient residencies for them, but about half of them were in CA and in the 1960s when the MD and DO physician organizations in CA merged all of those DO schools and residencies transitioned to MD schools and residencies. DOs struggled to get consistent training (which at that time was really just a rotational internship with very few actual residencies) and they were in a deficit since then. The AOA (and probably more so DOs) lobbied along with IMGs in the 1970s and 1980s to get access to ACGME (AMA and then, when it was established, ACGME) residencies, but generally they pushed more for expansion of their own residencies (which improved but never met demand) than interest in ACGME residencies.
Prior to the 1970s/early 1980s, people did not really go to DO schools as a back-up/back-door but because they believed in the goal/mission (or because their parents were DOs). That's why you'll see all these hardcore believers in that age group. It really wasn't until the mid to late 1990s that it truly became a place where the majority of the classes were made up of people that couldn't get into MD schools ("a backdoor"). And then of course like you said, schools proliferated, residencies (which already weren't sufficient) couldn't keep up even more, and about 12 yrs ago the AOA looked at ways to negotiate a merger.
The DO degree is a total misnomer. Over 95% of their education is allopathic and not OMT. Hence, their knowledge on OMT imo does not qualify for a doctoral degree. MD would be the correct degree for these DO students.
So interestingly (and I'm sure you learned this along with a host of ridiculous facts in MS1), Still never wanted a doctoral degree. KCOM was issued charter from the state for the MD degree, and he sent it back requesting a "Diplomat of Osteopathy" degree instead. Its only later that it was converted to a doctorate, I suspect to garner more validated or recognition in the eyes of the general public.
Also obviously "traditional medicine" in the late 1800s was problematic, so an alternative actually seemed reasonable, but even as early as the 1900s DOs were discussing merging the MD and DO degrees after it became clear that significant advances in pharmacology can really help patients (even before it was necessarily taught at all DO schools). This view was obviously pushed back upon by Still and the diehards. I believe it was either the president of the AOA or Dean of ASO (old KCOM) at the time that even mentioned it in a general address in front of Still (he was quickly replaced).
Anyway its all history and is kind of irrelevant now like you said. I don't feel strongly one way or another about changing the degree, because while it would be simpler from a public understanding standpoint, practically it doesn't matter after residency. While I don't care, I do think for students it would be more reasonable to have an osteopathic "certificate" and separate smaller exam alongside the USMLE for osteopathic school students than keeping things the way they are. I won't hold my breath for that one though.