@ThinkPositive Assuming you mean pre-10k BC and not the time of the roman empire, that's still 30kya short of the rough estimation of neanderthal extinction... And rather than a couple thousand, it's actually a few hundred specimens at best (Given the weird date bracket you used, I assume you are also counting the upper paleolithic, which is largely after the neanderthal extinction), with the majority being fragmentary skeletons (mostly of skulls).
As for the extinction, I agree that "the idea that you could eradicate someone that's spread out over an entire continent with little manpower and no reason to do so is quite preposterous", but that's not typically how it is hypothesized. The correct reasoning is that sapiens "didn't directly carry out a systematic genocide" but rather slowly crowded out the neanderthals from their habitats (whether it is due to conflict, be through direct fighting as seen here, or indirect through the loss of food and resources, or even climate change, is still debated), the neanderthal's habitat shrink enough such that they slowly die to traumatic causes (by carnivores or accidents) or starvation or even the lack of resources (such as inability to survive winter), and by the end, the population is bottlenecked enough that we DON'T need to murder the remaining ones for them to die out from a crippled genetic pool (susceptibility to pandemic) and the lack of viable mates.
That aside, back on topics of direct attacks. Yes, because "direct attacks might've occurred", largely because we lack a comprehensive fossil picture of the times, we cannot definitely say that "the theory that hunter-gatherers killed each other has no credibility whatsoever", which is the whole point I'm trying to make. Surprisingly anticlimactic in a sense, in the spirit of the old wisdom in English class, "always make sure to never say always and never".
p.s. On a side note, I do not know why you need to bring in a discussion of dogs domestication, and there are a lot of skips in logic linking brain size to behavior. (which while the brain do govern behavior, having a larger or smaller brain have no correlation with disposition for a specific type of behavior) Not to mention, wolves are not more aggressive, just more alert and suspicious of danger, thus making dogs the naive counterparts. Just be glad that it was the humans who found the naive dogs and not some predator, since I doubt the early dogs with their naivety will survive as long as wolves in the wild if it leaned to approach another species without any sense of danger.