The reason I do it, and it may or may not be valid but my thinking is it doesn't hurt is that most joint problems in old age are due to wear and tear on the joints over the years. If the supplements help repair that small wear and tear as it happens before it gets to the point of causing symptoms, then maybe the worst damage can be avoided or at least put off for longer.
There's no way to know for sure that it works but my first girl who had arthritic elbows was put on supplements at diagnosis when she was 8. I put our other dog who at the time had no symptoms and was 5 on them too, and he didn't need arthritis meds until he was 13 and actively competed in Obedience at the age of 10. Chloe's been on them her whole life and is still actively competing at 8.5. Would they have been okay without the supplements? Maybe, maybe not. Do they seem to be doing any harm? No. Is it worth the possibility of wasting my money on the off chance it's helping? For me, yes.