You are right. He did his lines and part as written, but it just did not pan out. And once they did a few episodes it was too late to retool the writing for his character.
I read in one of the Andy Griffith Show books that Andy and the producers thought Burns would fit in, but he just didn't work out, so they let him go. Andy said it was no fault of Burns and that he, Andy, took responsibility for what happened. I suppose this comes under the heading that nothing is perfect.
I read the same thing, Dr. Pendyke. It may have been as simple as Burns loud, northern style of comedy just didn't fit into Mayberry. It is really difficult to find anyone who liked the character. Not impossible; just difficult. There is a Warren tribute artist that shows up at the Mayberry events (Mayberry Days, etc.) and people do like him.
He was basically a stand up comedian and it just didn't work out, plus the character of Warren was kind of a pain anyway. They gave it a shot and it didn't work. I'm glad no one takes their dislike of the character out on the Warren tribute artist. :)
I think Jerry Van Dyke may have worked out well, banjo and all. I think they needed someone that was a bit different than Barney. Any kind of replacement with the same or similar character (inept but over-eager deputy) would always fall short - there could be no other Barney Fife!
With Floyd, they brought in Emmett, who I thought did a great job in a similar role, but much different character. And Floyd was perhaps my favorite character.
After Knots' departure, Jack Burns had some pretty big shoes to fill. He was a tough act to follow.
To me, Jack Burns never fit into the "endearing" kind of character we were used to...and I believe Jerry Van Dyke's character would have been "too high maintenance" over time...and you all are right. It was almost impossible to follow in the giant footsteps of Don Knotts.