Prince Charles has a wide ranging set of interests eg. architecture, painting, organic farming, conservation, classical music etc. etc. not one of his interests could have possibly overlapped with JS' interests. On what basis could they have been friends?
I can't know just how "friendly" they were, but from Savile's POV the obvious motivation would have been to lend himself an air of respectability - and maybe, like Peter Ball, to get a useful idiot on his side who'd speak up for him if he was caught out
Prince Charles has access to the most highly respected counsellors, therapists, philosophers, gurus and clergy in the world to discuss his emotional life. Why on earth would he value the judgment of a sleazy, creepy DJ who never managed to make any relationship work?
You might equally ask why he valued his associations with van der Post, Mountbatten and the already-mentioned Peter Ball among others
Perhaps it's because he's a judgement-free zone himself, and therefore vulnerable to manipulation by such folk - also why, in at least Ball's case, he's been officially criticised for it