Observation of prokaryote/prokaryote endosymbiosis would be real evidence against the rise of eukaryotes being the or one of the main limitations in the number of intelligent species in our galaxy.
There are no known modern prokaryotes capable of phagocytosis. Presumably the extinct prokaryotes who were capable, including those from the same lineage as the eukaryotes but which did not pick up mitochondria, were outcompeted by the eukaryotes who occupied the same niche.
Other changes like the origin of the cell nucleus and many other organelles can be readily explained by other malfunctionings of the phagocytosis process. Basically once you have the ability to pinch off parts of your cell wall into internal structures, you suddenly get a bunch of internal structures made of stuff that look surprisingly like cell wall.
There is also secondary endosymbiosis, where the endosymbiont organelles of one eukaryote are engulfed and incorporated into another eukaryotic cell to create a new type of endosymbiont. This has happened at least 8 times.
There are also theories that some other organelles are the product of other endosymbiosis events, many of which also have some of the hallmarks like their own genetic material. These theories are more speculative though.
It's also worth noting that while eukaryotes obviously gained some important capabilities from incorporating these endosymbionts, the endosymbionts they incorporated obviously managed to just evolve to perform those functions directly. Further, while one of eukaryotes' distinguishing features are mitochondria, there are several other major differences, and mitochondria are not believed to be what made eukaryotes better able to evolve complex multicellularity. Prokaryotes have indeed evolved multicellularity dozens of times, and we arbitrarily set our definition of complex multicellularity to distinguish from what prokaryotes have achieved.