Apologies for replying so late, the reason was my long travelling.
@Trof, I think you brought quite a valid point. I myself did not pay attention to the detail that existense of centromeres is@exactly the difference between the scenario that I described and how it actually develops in the nature.
@Pito, it is just quantitatively bigger number of combinations, mathematically it is not - whatever combination you get at the end of meiosis, you could get by recombination between homologous chromosomes right away.
If it was up to as many combinations as possible it could be 2, 3 or more replications. But everywhere in the nature meiosis works exactly the same - one replication, 2 divisions, 4 resulting genotype combinations. So it has its causative reasons.
Not sure I get you or you got me.
If you have 2 divisions you have 2 chances of getting a recombination of genes.
With 1 , you have only 1 divisions, so les chance of having different combinations.
You have a more diverse "offspring" when you use 2 divisions compared to 1.
Not sure how you can say that this is not true mathematically.
1 division= 2 gametes
2 divions = 4 gametes.
4 > 2 ... so not sure what you mean with it is the same mathematically.
Also: homologues recombination is not the same als the splitting of the homologues.
And: why does it have meiosis and 2 divisions and not 2 times meiosis or X times and X divisions to have even more recombination (and gametes?) => every system is limited , it is a trait off between more "recombination" (more options) and more chance in mutations.
The more you mess around (more divisions and so on) the more chances you have for mutations.
So nature just somehow evolved to a system that gave the best option.
However (!) not all organisms work with meiosis. Certain fungi for example do not use this system and have a system more like you are explaining.
And it turns out their rate of recombination is higher! They have a lot more of (random) recombinations, so even more differences in their genes for the offspring.... And it turns out that for those organisms it is a HUGE benefit because they have so many different daughter cells that there will always be a few adapted to certain conditions.
The disadvantage is however also a huge loss of cells that got stuck with a bad set of genes.
Imagine this in humans => with our rate of an average of 2-3 babies per family we wouldnt survive for long... however for those fungi it doesn't matter because they make millions of "babies" so they can afford to have this type of recombination.
One can question whether the start of meiosis (sexual reproduction) is part of the evolution towards humans....