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.
Energetics and thermodynamics are absolutely capable of imposing harsh boundaries. How long has our battery technology been stuck at this order of magnitude? How long have internal combustion and explosives been stuck at this order of magnitude? A long time, and that's with an enormous number of very clever and motivated people chipping away at the problem.
There's a reason why I chose distributed systems in my analogy: it proves that information science and engineering are not immune to the "difficulty barrier" problem. Vertical scaling hit a soft limit in the software industry long before it enabled the largest cloud-scale applications we see today. The transition from vertical to horizontal scaling was painful, but not nearly as painful as it would have been to wait for vertical scaling to catch up. We'd still be waiting.
This is what I'm talking about. Your making an assumption and straight up saying it's an assumption, but not providing any evidence that this assumption is true. You make another analogy which may or may not apply. I'm not saying you're wrong, and I'm not saying that you're right. I'm saying there is no possible way any of us can know at this point.
The "you can't prove it" objection must be checked at the door for the sake of keeping the speculation interesting. Nobody is arguing that you should walk through the door. It's probably more respectable to refuse, on the whole. Once you walk through the door, though, complaining about proof is a bit silly, like walking into a speakeasy, ordering a drink, and complaining that they have served you illegal alcohol. It's not wrong, but it's also not helpful.
The evolution of eukaryotes is based on the specific path that Earth went down. The combination of RNA, DNA, proteins, and other cellular chemical building blocks are a way that a cell could be constructed, but not the only possible way a cell could be constructed. For an extreme example, we could have non-carbon based life. If that is true, then all of our assumptions about what is scalable and what is not, based on our biochemistry simple cannot be trusted. So, looking at how long it took for something to develop on Earth tells us basically nothing about how long it would take to do that with this other biochemistry.
There is a substantial body of abiogenesis experimentation focused on reproducing DNA/RNA proto-life. They haven't managed to make anything that self-replicates, but they have managed to make nucleic acid polymers with catalytic activity, e.g. you zap the primordial soup with lightning, you get a bunch of short sequences, some of those sequences fold into RNA-zymes that catalytically produce long "AAAAAAAAA" sequences or long repeating "AUAUAUAU" sequences. The critical next step is to demonstrate the ability to do this from a template.
In any case, are you aware of research that aims to do this with alternative polymer chemistries? Such results could inform our speculation about the likelihood of a fundamental 1000x difference.