Numpty question but why fit an underdrive pulley to road engines?

I can see the point in a higher revving race engine (water pump cavitation, alternator overspeed) but people seen to fit them to fairly standard engines.

What other advantages am I missing?

Just a guess, fuel economy or to prevent a known problem?

specific engine may have a good reason, but I guess for the most part folk think it must be better because its what race engine use.....

When I ran high revving x-flows (8500 rpm) I still ran standard diameter crank and waterpump pulleys and never had an issue with cooling. I did run a slightly bigger alternator pulley to slow the alternator down a bit which resulted in better alternator life but the warning light did stay on at idle sometimes, not an issue, once the revs were raised it went out.

I fitted a underdrive pulley to my engine and had to change the alternator pulley as well. The alternator would not charge on idle as it was going to slow. Red light kept coming on and it killed my alternator after time. Fitted Smaller pulley which sorted the problem out.