We have nearly all species of bacterium/prokaryotes in every known niche and climate on earth right now. So we know they all survive in these predictable cycles yet they remained single celled.
Query: up to now you have been talking about the prokaryote/eukaryote transition. Now you speak of prokaryotes remaining "single-celled". It is true that multicellularity has occurred only in eukaryotes, but I am sure you are aware that many, if not most, eukaryotes are single-celled protists. IOW the emergence of eukaryotes per se and the emergence of multicellular eukaryotes are distinct events that did not occur simultaneously, nor under the same circumstances.
So to my way of thinking weather as a specific could be discounted as a causitive agent in stimulating evolution to a muliple celled form.
Don't be too quick to dismiss the weather, or rather the climate as a causative factor. And remember that the biosphere affects the atmosphere and the climate. James Lovelock, originator of the Gaia hypothesis, surmises that the production of free oxygen by photosynthesizing cyanobacteria may have precipitated the first Ice Age about 2.5 billion years ago. The higher levels of atmospheric oxygen were already a challenge to life that had arisen in relatively anoxic conditions, and together with the lowering of average temperature may have produced the conditions favoring nucleated cells.
Lynn Margulis has done a great deal of work on the possible symbiotic origin of eukaryotes and their organelles.
BTW, I am simply asking an honest question here. To my knowledge there is no published literature on why this happened. I am just trying to use simple logic and my knowledge base to determine the plausibility of the way some say life diversified from a single cell life form. If you don't want to participate that's ok. Thanks for what you have written so far.
So, as Mallon said, you need to check out what is available on the diversification of bacteria themselves. Why do we have cyanobacteria, proteobacteria, firmicutes, sulphur bacteria, methanogens and so many different types of bacteria. We need to remember that bacteria are as diverse if not more diverse than any vertebrate order.
Then, if you want to venture further, look at the work of Margulis and others on the emergence of eukaryotes.
And finally, at the origins of multi-cellular life.
The rest is pretty much a piece of cake.