they were a language isolate, which is usually how we figure these things out. so, we know they weren't indo-europeans (persians, greeks, russians), and we know they weren't semites (jews, assyrians, babylonians, arabs). further, all evidence is that the people we call akkadians were indigenous semites, and the sumerians were an invading class that came in from somewhere else. over time, the akkadians took over the society from the inside, and we have the historical period of ancient semitic rule, which was actually comparably short, following from that.
the persians came in after that, who were replaced by greeks and romans. it wasn't until the arabs came out of the desert that the region was re-semitized. and, as mentioned, the mongol invasions were vicious - the turks came in not long after, and are a dominant genetic contributor in the region, to this day.
so, semitic rule north of the desert has occurred from time to time, but it is by no means the historical norm. it has generally been short-lived, compared to the longer indo-europeans and turkic periods of rule. nor is it correct to argue that the areas to the north of the desert have semitic indigenous populations, as most of these areas actually don't.
so, it's not weird to point out that the sumerians sure looked white, as we state with clear certainty that they were not semites. the caucasian groups are thought to have been there, just to the north, since the ice age. it's not hard to put together a migration hypothesis, of some caucasian language isolate moving south.
but, the sumerians.....their art is hard to put in context. they really don't look like much of anybody at all, making you really wonder.
what does this person look like, to you?
that person doesn't look very semitic or very dravidian, that's for sure....although i am sympathetic to elamo-dravidian, even as i am not to sumero-dravidian. i suspect the migration flowed into india, though, and not out of it. it doesn't help us understand sumerian origins.
do they look libyan? not particularly.
that person looks slavic, to me - russian, czech. maybe even east german.
or, how about this:
they almost look irish, don't they? but, they look kind of weird, really - unique. white, though.
this is another weird statue that looks almost british, but also looks kinda amphibious, eh?
you'll tell me i'm looking too much into it, and i'll agree to a point:
1) you can't discard the evidence outright. they clearly look white.
2) do you have a better idea? and pause before you start - i've read some of them, and don't think they're actually very good ideas.
we have this subconscious bias in western science, that we don't want to stray too far from the bible. consider the charlatan colin renfrew, for example, who built a ridiculous theory to replace the gimbutas theory that is basically just the tower of babel - and that it took decades to fully debunk and throw away. so, it's hard to imagine that the people of the flood might not have been "jews", but might have been....white.
but, we must always follow the evidence.
and, it's clear enough to me that the sumerians came from the caucusus, which us how they ended up as a language isolate.