Meadowhall is always full when I get there. Since using Centertainment I have always managed to find a spot, even if a long way from the tram. The Cinema and any other licensed premises require licenses and planning permission for road access.
My employer is near City Hall and has around 20 under ground parking spaces but employs around 70 people. There are not enough car parking spaces in the centre even if they were affordable. Have you ever tried to drive out of the middle of Sheffield on a weekday between 4 and 6:30 pm?
Sheffield needs park and ride on the tram routes. They have just knocked down a perfectly good arena. Ideal place for a park and ride car park.