The only thing I could find is that the community switched form one hydrogen atom to 1/16 of Oxygen-16 (which they thought to be the only isotope that exists at time because they had no concept of isotopes yet) even though they were approximately the same value was because oxygen "was more amenable to experimental determination" (https://en.wikipedia.org/wiki/Dalton_(unit)).
That's from Wikipedia, so I am still skeptical. If that is the case, what about oxygen allowed it to be more amenable to experimental determination?