I am an Assyrian. Most Assyrians look Semitic, I and my close family members have dark hair as well as blonde hair and red hair (and naturally bald too lol). My father is light brown skinned and is green eyed, but my mother is very light skinned (pale) and does not look Semitic. Both my father and mother had blonde haired grand parents. Several of my cousins are red headed. I am probably the most Semitic looking of all of them yet am oft mistaken for being otherwise. We are never as dark as gulf Arabs and we are usually tall. My mothers grandfather was about 7 feet tall, muscular, broad shouldered, blonde haired and blue eyed. This is by no means a generic Assyrian and should serve to demonstrate that Assyrians carry a very wide range of appearances. We look more like Armenians than anyone else (except we tend to be taller based on my experiences). We also resemble Jews and share their variety in appearances.
Historically Assyrians have mixed with quite a few Semitic and European populations but we are primarily descendants of (and have identified as) Akkadians (Semites) Aramaeans (Semites) and Sumerians (who are native to Central and southern Mesopotamia, spoke a language Isolate and have a unknown racial group although it is almost certain they are a caucasoids. Due to slavery, rape and assimilation by immigration and annexation, many surrounding peoples such as Amorites (Semites), Elamites (another unkown racial group that is presumably Caucasoid and speak a language isolate) and Hittites (Indo_European) and Hurrians (Indo-Europeans that encompass the Mittani and Urartians) have notably contributed to our gene pool. Historically, Assyrians would have dealt more with Indo-Europeans than Babylonians however, they never considered each other different racially or culturally except by political or religious affiliations. All surviving Assyrians and Babylonians are the ones who lived in or moved to the northernmost parts of the homeland who all eventually called themselves Assyrians (following the collapse Neo-Babylonian government)
This video demonstrates a variety with a Semitic based appearance that well represents Assyrians (including those who use the misnomers Syriacs or Chaldean). Second link is a bit extra.
https://www.youtube.com/watch?v=qk7Gyrg25VA
https://www.youtube.com/watch?v=E2UVRd7NbDsA
As for any Neo-Nazis, Assyria and Babylonia are the heirs of Sumeria and Akkadia, All of the which, have achieved so much that only few countries can possibly rival them in their contribution to technological, scientific, martial and literary advancements. If taken as a continuous civilisation, it is probably the greatest one the world has ever seen. They were however almost if not completely void of European blood for most of recorded history (which began with them). The late European contribution to the Assyrian gene pool did not seem to demonstrate any particular effect on the progress and and achievements of Assyrians. Furthermore, surrounding Europeans peoples like the Hurrians (the Urartians and the Mittani) and the Hittites were heavily influenced by the Assyrians and eventually had large portions of their populations absorbed by them. The aftermath can even be seen in Greeks referring to the Cappadocians as "white Syrians" (meaning white coloured Assyrians). Traditional Middle eastern, Armenian and Greek dancing and religion both have Mesopotamian roots. Many famous ancient "Greek" thinkers turn out to be not so Greek such as Lucian of Samosata or Tacian, who were Assyrians writing in Greek. Others like Thales of Miletus were educated by an Egyptian tutor since childhood. Pythagoras copied the Pythagoras theorem (which was a well known fact in Mesopotamia for well over 1000 years before Pythagoras) from Babylonians and introduced it as his own upon returning from a trip to Babylon and Alexandria. Aristotles nephew oversaw the translation of Babylonian texts into Greek as Alexander marched through Babel. He supplied Aristotle with the translations which he used to study. The list goes on...Western civilisation began in Mesopotamia and Egypt....went to Greece...then Rome...then Europe. So it is not as much a history of superior genetics (as the Neo-Nazis would have it), it is more a matter of superior culture which has created superior societies. When the better culture is born, the lesser will generally succumb to it. However, I do not reject genetics as a factor of intelligence and strength, it merely appears negligible considering that In Mesopotamia in 2100 BC, the Epic of Gilgamesh was written (a remarkable piece of literature that indicated writing must have existed there some time well before it). Whereas In Germany, writing came about in 800's BC. yet today Assyrians are dying out quickly and without a homeland altogether whilst Germany is one of the most powerful nations in Europe. I don't see a any case of genetic superiority. From looking at the history of various caucasoids with distinct appearances and cultures, it seems to primarily be a combination of culture, resources, environmental factors and knowledge that make advanced people from among them.