Saying that the subsequent animals in the fossil record “competed more effectively” is an unobserved statement.
Who is to say that the Neanderthals are not antediluvian humans? More conjecture by exclusion.
Uniformitarianism is one big problem with modern “science”. It is pure dogma.
The scientific question would be: can we say anything about why Neanderthals disappeared?
The answer is: "nothing direct", but we can say that it only happened after modern humans appeared nearby.
We might note that modern humans appeared more fleet of foot, handier with tools, maybe better with language, and with a passion for art work.
So something gave them a critical advantage, and Neanderthals disappeared while human populations expanded far beyond Neanderthal numbers and range.
And there are only a few broad choices for why Neanderthals died -- 1) hunted down and exterminated by humans, 2) died of human carried diseases 3) habitat destruction by humans, meaning the large animals Neanderthals hunted. 4) Humans ingenuity allowed their populations to grow to the point there was just no place left for Neanderthals to live.
Now you could look for evidence of each explanation, and select the one(s) evidence seems to support.
That's science.