The point of percentile dice isn't to generate a string between "0%" and "100%", it is to test if action with chance of x% success gets done or not. For every other value of x, there are x out of 100 values which are strictly less than x, or if you count 0 as 100 then there are x out of 100 values which are less than or equal to x. Either way you get x% percent chance for event to happen. If the dice had 101 sides, the probabilities would be x/101 which aren't nice round percents.

It even works correctly for 0% and 100% chance events. Assuming 0 is counted as 0 - For 0% there are 0 numbers less than 0 on dice so chance of throwing number less that is 0/100=0%. For 100% all 100 numbers are less than 100 so no matter what the result of throw is you will succeed.