Why assume he is an "outsider"? He may simply have been part of a royal, priestly, or royal caste that practiced some degree of endogamy. A consummate "insider", in other words, who traced back to the founding of the original settlement. Or, perhaps he belonged to a later group that brought the metallurgical arts from the Levant, spurring trade and, thus, wealth, at least for some, at the top. He could have been the son of a "lord" and a concubine, who rose to the top through military exploit.
Nor can we assume that the society's economic basis was stable and invulnerable to disruption. Surplus wealth would have been accumulated through trade or warfare. Drought could have undercut the ability of the society to feed itself. Disruption or severing of trade ties, with suppliers (sellers) and/or customers (buyers) could also have been a driver. Towns could also have fallen into internecine warfare over over-farmed land, leaving them vulnerable to being picked off by an external force, one-by-one.
Interestingly, 4200 BC, which was about when Varna collapsed, corresponded with the rise of the Akkadians in the upper Tigris/Euphrates, liberating them from Sumerian suzerainty:
https://en.wikipedia.org/wiki/Ubaid_period
"North Mesopotamia" is, of course, Akkad, although long before it became an empire, superseding the Ubaids throughout the region. Still, if it succeeded in seceding from the Sumerian/Ubaid "union" around 4300 BC, it could have disrupted far-flung trade links and routes, perhaps being the tipping point that caused an "outpost" such as Varna to topple (and which was possibly already ripe to fall).
I agree that there is no need of a steppic juggernaut to overthrow a society that may have already long since seen its best days. No invasion would have been necessary - only the inability to keep the cattle, goats, and sheep of interlopers out of the "fields", breaking the link between "town and country", without which no civilization can persist.