Older boilers fired up on maximum burner rate. They controlled the water
temperature by switching on and off. A modulating boiler can reducing the
flame size. So assuming the output and heat exchanger are the same, there
will be no difference in heat up time.

So what's the point of the modulating large and small flame?

Isn't it to control the rate of heat?

My old boiler wouldn't modulate and would heat on fixed flame which would be
lesser then a full on modulating one in my new boiler, which would surely
heat faster on full modulation?

A bigger flame means quicker heat doesn't it? Or is my sense of logic not
modulating right?