“exclude mountain bikes as they are quicker to ride”
On a typical cross course, I think a cross bike would be a lot faster, certainyl not slower than a mountain bike. You wouldn’t benefit from a mountain bike’s wider tyres, suspension or better brakes.
Skinny tyres are great in mud and cross courses often have tarmac sections. Good brakes aren’t really needed, although decent frogleg cantis are pretty good. The drop bar position just lets you pedal harder.
They’re not nearly as rubbish off-road as you might think. The big wheels, skinny tyres, drop-bar position and big gears just make you want to go very fast.