@Firefliess
I don't think that's quite how mutations happen @tree. It's not something that happens gradually over lots of generations. The mutations that have caused us problematic new strains have occurred by chance just in one person - possibly someone with a weak immune system who takes a long time to fight the infection off.
If significant mutations of concern are developing in immune-compromised people who have been brewing the mutation for months then arguably a sharp and fast wave would be no different to a shallow and slow one.
However, our belief that variants of concern can develop in those with immune conditions precisely because they play host to an active virus over a long period of many months indicates that it does indeed require many, many generations to achieve sufficient mutation to evade the original virus.
At the core of evolutionary theory is that random mutations occur in each generation and that these compound and further compound over time. Time is absolutely key.
In the same way humans didn't spring from chimp-like apes over just a few thousand years, so Covid won't (or is very unlikely to) mutate from an Omicron to a Pi (next Greek letter) variant over the life of a single ten-day infection!
Notwithstanding the impact of immune-compromised individuals, 100,000 infections per day over 10 days would seem far less likely to generate a radically different variant than, say, 10,000 infections per day over 100 days, despite the fact there were 1,000,000 infections in each scenario.
That's why I think a sharp and fast wave is less likely, or certainly not more likely, to lead to another variant than a slower wave whose curve has been flattened.