His sitcom aired at a rough time in American history. 1964 to 1969. Vietnam. Assassinations. Riots.
Nabors' character was a sweet and innocent oasis, a purely good and nice person. Gomer might have driven SGT Carter insane, but you never doubted his heart.
I don't watch much television these days, and I can't think of another character that comes even close to Gomer's characteristics. Every current character is flawed in some way. Flaws can be funny. It's the story of my life.
Simon & Garfunkel sang "Where have you gone, Joe DiMaggio? Our nation turns its lonely eyes to you." You can replace Joltin' Joe with Gomer.
We can all use a little Gomer these days.