Simple math will show that for 50% of the population, a half-size will be closer to their “true” size than an integer size. 

But that means it won’t make a difference for the other 50%. 

We can’t tell which half you’re in. 

P.s.  this assumes that the sizes of human feet are a continuous rather than discrete range. This is not a trivial assumption as long-term wearing of discrete (integer) shoes may deform half-size-feet into a shape closer to integers.