I always thought that this type of thing was down to policing. If a club makes it all ticket they can plan for X number of police/stewards. If they allow pay on the day then they could be under staffed should more people attend than expected.
I get that this doesn't apply to every game but being it's a low priority fixture (checkatrade), maybe Mansfield cannot estimate how many people are going to attend so to keep policing costs down they are requesting attendee numbers up front.