Not the original commenter and agree with your sentiment.
That said, from what we know about random graph models, once the transmission rate passes a certain threshold, the cumulative number of eventually infected individuals will NOT scale exponentially as the transmission rate increases.
You're speaking about initial growth rate though, not convergent size of the once-infected population, which is definitely exponential and relevant if you care about minimizing simultaneous hospitalizations.
That said, from what we know about random graph models, once the transmission rate passes a certain threshold, the cumulative number of eventually infected individuals will NOT scale exponentially as the transmission rate increases.
You're speaking about initial growth rate though, not convergent size of the once-infected population, which is definitely exponential and relevant if you care about minimizing simultaneous hospitalizations.