The main reason that you would use a higher class of IP would be so that you could more easily subnet off a range of IP addresses. For instance, a customer of mine recently installed about 40 IP cameras in 5 different buildings. They put all of the cameras on 172.16.12.x. By having all of the cameras in the same 12.x range it was easier for them to group devices together. It also made it easier for subnetting. They could subnet off the entire 12.x range of IP's so that normal users couldn't see the cameras from their workstations since all of the workstations were on 172.16.10.x. It's much easier than using a class C and figuring out different netmasks for different users.
The other main reason to use a higher IP class is that you need more IP addresses. The only real difference between the IP classes is the number of IPs in that class. Class C has 254 usable IP's, where a class B has 65,534 usable IP's, and a class A has almost 17 million. You could set up a 10.x.x.x. for your home network if you really wanted to. When you have 17 million computers in your house, let me know and I will fly to the UK personally to see it
