Precisely so. Producers may have had experience 'in the scene' of their youth, but were now quite distant from 'the scene' because of their work. They were imagining what the current youth generation liked. It's like hearing a middle aged DJ trying to sound like a teenager by using outdated slang. It sounds stilted because they're not of that generation.
Savile's popularity and ubiquitous appearances weren't only engineered by the man himself, but by a self-fulfilling situation:
Savile was everywhere on TV so he must be popular so we must put him on TV ... and another producer carries this on. This circle-jerk only lasts until someone comes to their senses and says "Hang on - he's not actually that good, is he?"
You're right. I lived near Leeds so "heard the stories" re Savile - someone would know someone who was a nurse at the hospital where he was a porter, or something else... And we wondered why nobody in London seemed to know what he was. There was a fashion for the media to have pet Northerners, as well, at the time - certain Yorkshire actors would appear and re-appear in what felt like every show... they still presented the news with plummy RP accents but from John Noakes on, Yorkshire accents seemed to be one of the things that maybe TV producers down South fixated on, if they wanted what they imagined to be an approachable, safe, "everyman". We forget it now but at the time, it was very prevalent. I can remember feeling suspicion about these "professional Yorkshiremen". (Not Noakes, actually, but pretty well every other one!) Hard to put into words but I do think if the posh BBC wanted you to trust or believe something, in the late 60s onwards, and they didn't want to do a Mr Cholmondley-Warner type person, they'd substitute, in a condescending way, with a token Northerner. This was my perception even at the time, as a little Yorkshire kid! But think about it, we were fecking everywhere on BBC in particular, even when other regional accents hadn't yet broken through very much... Savile fitted this mould.
ETA: I did a bit of genealogical sleuthing a while back, as my family came from the same Leeds backstreets and Id noticed were neighbours to Saviles, at one point, just curious if those were any relation to Jimmy or not. I couldn't find a link but I did find Savile's family in the censuses and despite being a large family, dad had a fairly middle class job, IIRC - so not even sure that dog rough Leeds accent he did wasn't a bit put on. Interview I saw with his mum, she certainly didn't sound as stereotypically Leeds, as Savile himself did.