As you pointed out, liquids reduce a lot faster when you crank up the heat compared to when you leave it at a gentle simmer. The reason is simply that you're introducing a lot more thermal energy into the liquid when you crank it up to the max. Once the liquid reaches the boiling point, any extra heat you provide will be canceled out by the cooling effect of evaporation. So adding more heat to a boiling liquid causes the evaporation rate to go up while the temperature stays the same.
As for the reason to use a simmer, that's going to depend on the liquid. Some liquids handle heat a lot better than others. A simmer is nice to avoid burning, curdling, boiling over, etc. But if you're reducing something that can take the heat, feel free to crank it up.
Liquids that shouldn't be boiled include: anything with a lot of milk (can scorch or boil over), anything with a lot of starch (can boil over), emulsified sauces (can break), chocolate (can scorch), oil (very hazardous when boiling), and custard (can curdle). Some people also prefer not to boil stock because it can become cloudy, but that doesn't necessarily ruin it.