I watched one of Rich's earliest fill-in episodes on YouTube not too long ago, and had to double-check the credits to make sure it was actually him. His style was much closer to that of Johnny Olsen--conversational, yet authoritative, and a much more reasonant tone. If he had kept this style, I'd miss him a lot more.
But something happened to him in the next three years he announced with Barker, and by Bob's final ep. he just came off as annoying--his nasal, bombastic inflection threatened to ruin the show at times. I remember reading that Roger was coaching him and giving him pointers on how to improve during this time, which is great, but it seems like he took said advice the wrong way.
As Steve alluded to, Rich was apparently let go due to pissing off Mike and/or the other senior staff--a situation he knows more about than I do. While I don't doubt his story, I do think the show unfairly tried to turn him into a comic foil with the "Drewcases" and he just wasn't cut out for it at all--he's a TV weatherman, not a comedian.