In addition to exclusivity clauses (which tend to give benefit to central university finances at the expense of individual departments*), purchasing like to be in control of the process and the supplier list for a few reasons, most of which apply at least to some extent to big businesses as well.
Universities often have labyrinthine purchasing systems and try to impose significant conditions on all contracts. Both of these can cause hassle for suppliers as well as staff. So purchasing want to make sure the suppliers can deal with this (as well as not going out of business taking the money with them.
For some purchases, particularly as public bodies, universities have to follow certain legal procedures (multiple quotes, public tenders etc.). While this doesn't inherently require that the suppliers are restricted to a list, in practice there's a whole supply-chain management system that does.
The good news is that it's often quite easy to get a supplier (of low-value items at least) added to the list; it can be much harder in industry. And the right people can work wonders when it comes to getting round some of the other difficulties.
*"If you buy all your PCs from us we'll give you a massive discount next time you upgrade your library computer room (but we'll charge a small fortune if someone wants a CAD workstation or a machine with extra slots to talk to hardware)."