The problem has nothing to do with having a nucleus. That's the solution. As you note, it's possible to imagine other solutions. The problem is dealing with gigabytes of genetic data instead of mere megabytes. Typically one would use units of base pairs, but in the context of talking about potential alternative forms of life I'd argue that units of information are more appropriate. In any case, the "easy" strategies suffer from a severe dead end that prevents them from going beyond a few megabytes. Lots of things go wrong at that limit, and while other forms of life would encounter those obstacles in slightly different places, the problem of "simple strategies that don't scale" is almost certainly universal.
https://upload.wikimedia.org/wikipedia/commons/e/e4/Genome_s...
Eukaryotes, in contrast, scale.
It's not an easy task. The strategies are highly elaborate and severely intrusive. They touch the most fundamental, highly conserved aspects of the genome, of cell functionality, and of reproduction. Genes have to be organized hierarchically, packed and unpacked, and everything that interacts with them has to be made compatible with that reality. Further, everything must be done in parallel. The entire architecture of the genome changes as a result. It's like a distributed system vs a monolith. It's a tough, deep-reaching transition to pull off, it's a tougher transition to justify, and that's if you're an engineer capable of things like planning, prediction, and delayed gratification! A greedy optimizer bumbling around in the dark can't rely on cognition (or even a hype cycle!) to propel itself from one mountain range of local optima to another mountain range.
I'm sure there are plenty of strategies for scaling genomes, but if they're all difficult -- and the crazy elaborate mechanisms we see in Earth eukaryotes suggest that could be the case -- then they still constitute a filter.
But yeah, this is all speculation. Nobody really knows.