However, whatever it was, it would not be expected to have a minimal gene set for whatever it was, would it ? Simplicity is more an aim of design rather than evolution. Once evolution gets going we should expect more complexity than is strictly needed.
Yes, but as I stated earlier, there is nothing at all stopping some early population composed of self-replicating molecules from branching off and diverging into Archaea and Bacteria - under the non-telic model. But under front-loading, you have to load the genome with functional but unnecessary proteins. FL doesn't work otherwise.
Isn't your argument that there genes going back to the LUCA which are NOT part of a minimal set ? Surely homology tests will - at most - show if the LUCA likely had a homologous gene or not ?
Homology comparisons between a eukaryotic protein and a prokaryotic protein will determine if the two proteins are indeed homologous; to determine if the prokaryotic protein was part of a minimal set (i.e., that it evolved from a protein that is necessary for the existence of life), we'd need to trace the homology deeper and see if it shares any homology with proteins in prokaryotes that are needed for life (such as DNA replication machinery, etc.)
Suppose that rather than there being NO minimal gene sets that allowed for the evolution of life that we see today there were a VERY FEW - a very small proportion - that did. Wouldn't then, a LUCA with one of those gene-sets be entirely compatible with the concept of front-loading ?
The issue isn't so much about whether a minimum gene set could allow
the appearance of the taxa we see today. Given an initial genome that only has the most crucial proteins to life, evolution could have taken many different directions - including the direction of life forms as we see them today.
However, if the front-loading designer(s) intended for a specific outcome, you'd have to load the first genomes with proteins - like globins, tubulin analogs, etc. - such that evolution would build on those proteins and the future of evolution would be shaped, and the origin of animals and plants would be much more likely. That's why you'd need to load the initial genomes with unnecessary (but functional!) proteins.
For it to be a prediction, you have to show that a minimal gene set doesn't provide the flexibility needed - especially given the time available - and you haven't done that.
A minimal gene set could evolve in a plethora of directions - including plants and animals. But, speaking from a probabilistic standpoint, with just a minimal gene set, the odds of animals and plants appearing on the scene are quite low, since there are many alternatives. For example, how plausible is it that SecY (which is, IIRC, a protein essential to all life) will evolve into hemoglobin, since they are not at all nearby in sequence space, and there are a multitude of possible proteins SecY could potentially evolve into. And this means that the animals you want to appear on the scene of life will very probably not appear. However, if you load a genome with globins, then it's quite likely that some form of blood will evolve, allowing the appearance of animal-like life forms.