Russ, most of the wonderful singers you happen to have mentioned were mostly dead before headset mics were invented for anyone other than telephone operators.
And, I loved those voices, too. However, you are now talking about individuals that really didn't need a mic at all to sing - they had incredible vocal control, and I sincerely believe a lot of that came naturally. Personally, I think Elvis probably had one of the best singing voices ever. I thought it was much smoother and cleaner than Sinatra's, but I loved those wonderful tones produced by Mel Torme even more than Elvis or Sinatra. And for fantastic country vocals, I thought Marty Robbins was right at the top of the list. But, what the Hell do I know.
In my case, I had to work damned hard at vocal control, and my first experience at this was as a radio newscaster on WHRF Radio in Bel Air, MD, then WCAO, and finally, doing voice-overs for WBAL in Baltimore. No pull away effects, no one riding a board, just voice control. Like said, a headset mic is not for everyone, Neither is a handheld!
Cheers,
Gary