It seems that anywhere else in the world, people with their own language would form their own ethnic group. But people in Southern China are all Han like Northern China, regardless of the many different languages. Why didn't a split develop?
two-part tl;dr:
They did
The Han thing is kinda huge, and not an easy force to go against, and anyway generally it was better to be Han than whatever else you might have been.
I'm out and about at the moment so this won't be crazy long but do feel free to hit me up with follow up questions and I can address them later.
Anyway, to expand on the tldr, in fact these groups did very much develop very much separate ethnic identities, but for a number of reasons, it didn't last into the 20th century.
Two good examples of this: Jiangnan/Wu culture in the Yangtze delta area, and the Hakka in South China (etc etc etc). Each have their own distinct (Sinitic) language. Each have their own distinct architectural styles, their own food, their own traditional song (山歌) styles, and the like.
However what happened in the late Qing period was this sort of from-inside-to-out shift in the educational system where the Qing government decided that the best way to make people think of themselves better as a part of the Empire would be for them to learn about the country starting small and then moving to bigger and bigger divisions. This meant starting with the village. In South China, this got dirty quick, as each local area published their own gazetteers giving the local history. The Hakka who were already well marginalised were written as villains, often referred to by derogatory terms, and, most importantly to this question, as non-Han. The idea of Hakka being or not being Han was huge in the lead up to the May Fourth Movement as Han Nationalism had become a force in its own right. If the Hakka are not Han, they can be dismissed as ethnic minorities so often are in Asias history. If they're Han, then it affords them a certain status.
Through written accounts of the time we can see a fight unfolding on precisely this issue, with the end result being what we see today: Hakka are unquestionably Han. However, of all the sub-ethnicities in Han (which is very much like "white" in the US in that it's made up in the sense of being "anything not a tagged minority"), Hakka has maintained a separate identity that we just don't see in Wu or Cantonese communities to the same degree. You could argue that sub-sub-groups like Teochew show this, but Hakka are otherwise somewhat unique in this regard.
In the Jiangnan area it's a bit tougher because assimilation has been much stronger there, and while there's still very much a Jiangnan culture that we can point to in things like the language, architecture, Huai-yang cuisine etc, it's definitely not as "other" as alternatives.
I personally would today consider the Hakka their own ethnicity that falls under the Han umbrella, and would say the same for Jiangnan culture. The only thing is that the perception has shifted toward "we're all Han" with things like Han chauvinism (often talked about but not at all new) being so strong, especially as the Qing deterioration was in effect.
So, yeah, they did develop sub-ethnicities, but the notion of being Han took precedence, again as we could say the idea of being white took precedence over various differing origins of people in America.
Like I said let me know if you have follow up questions. I'll have more time to cite stuff and expand on this later tonight.