What's the big deal about testing relays?

Fan relays usually include an internal fuse. If you still have the original black relay, the fuse is not replaceable. It's a good idea to replace these relays with a newer relay with a fuse in the top.

Climate control is complicated...you will have a Klima relay that controls the compressor. Bench testing the Klima relay is beyond the capabilities of most automotive shops, because it requires speed feeds from the crank sensor and the compressor sensor. To simulate this, they would need two signal generators. It's easier and cheaper to swap for a known good relay. There are two relays for the fans, and another if you have an electrical fan clutch. There are additional relays buried inside the fan switch, and lots of other electronic and vacuum controls. What is the problem with your climate system?