I know Regis more from when he presented a daytime show with Kathy Lee Gifford. He was such a character on that show that the co-hosts were secondary.
When I was at university, I had an American flatmate who happened to stumble upon Today with Des and Mel which aired on ITV at lunchtime in those days. She told me it was a total rip-off of Live with Regis and Kelly (as it was then).
I looked it up on YouTube and whilst ours was decent lunchtime fodder, I could see it was a pale imitation of Live, which had been on the air for many, many years. Regis just seemed so natural on-screen and the laughs/warmth he got from his guests and the audience came across as really genuine.