The small size of asteroids actually raised objections from quite early on. As early as 1802, William Herschel suggested that they be called asteroids because they were too small to be planets.I do wonder, however, if it is true that people were thinking along those lines then. Again: perhaps they were, and in that case I'd love to learn about it. But as far as I understand it, they were mostly concerned about the small size and relatively great number of what we came to call the asteroids. As I read it, the small size raised few objections initially, hence 'planet', but once it became clear there were a lot of them, objections began to be raised -- hence early voices already arguing against these bodies being 'planets'. But I also speculate that if there had only been, say, four asteroids and no more, they'd have retained the name 'planet', and few people would have cared that they basically shared the same orbit. What I'm trying to say is: concepts like "clearing the neighbourhood" or "dominant body" did become important later on, and for the very good reasons you mentioned-- and when they did, their relevance was implicitly seen in the 1851 decision, with which such concepts fit perfectly. But I suspect that in 1851, they weren't actually a deciding factor at all.
But from what I can find out from sources (mostly summaries rather than works published in the 1850s, those being hard to find nowadays) the presence of multiple bodies in a similar orbital zone also played a part, and particularly the prospect of many more bodies in that zone. So clearing the zone appears to be almost inevitable at that point.
The problem is that in the 1850s, there's no way to draw a line. It's not clear in the 1850s which bodies are in hydrostatic equilibrium and which aren't; telescopes aren't yet that powerful to do so reliably. So there will be a case of asteroid after asteroid being discovered and no-one being sure where to classify them. They're not even sure if Ceres is or isn't, and no real chance for the smaller ones. So the pressure will be along the lines of "all these things share the same orbital zone; whatever they are, they aren't planets".If I am right, however, about the state of such things in 1851, and we accept such a POD as possible (although I do not even consider it very likely-- just not ASB or anything), then you'd get a scenario where concepts like "clearing the neighbourhood" or "dominant body" never become a part of the definition of 'planet'. Not even implied. In fact, the opposite happens: certain objects that basically share one orbit (namely Ceres, Pallas, Vesta and Hygiea) are all called planets in that scenario! In this specific scenario, it is still possible that - after the discovery of increasing numbers of trans-Neptunian objects - 'planet' is redefined pretty much as it is in OTL. But given the circumstances, just going with "has achieved hydrostatic equilibrium" is also possible (unlike in OTL). That would keep Ceres as a planet (as well as Pluto). And yes, that would mean... dozens of potential small trans-Neptunian planets. Pretty unacceptable in OTL, but who knows? Perhaps acceptable in the ATL. (After all, I doubt they'd force kids to learn all those names in school.They'd just call them "the trans-Neptunian planets". Maybe mention Pluto by name.)