The guys you mentioned were all well established at the time they lost a good amount of hair. If they had lost their hair in their early - mid 20s they would have fallen off the grid.
Lennon had essentially a full head of hair at the time of his death. Look at the photos on the two virgin disc, which was his last one:
http://www.amazon.com/Double-Fantasy-John-Lennon/dp/B00004WGEK
Simon and garfunkle both had hair a good way into their careers. Simon wore a piece for awhile.
For Elton John's Honkey Chateau he had a little thinning so they hid his head:
http://www.amazon.com/Elton-John-Honky-Château/dp/B000001EGE
Elton's pic isn't even on the cover of Don't shoot me I'm only the piano player:
https://www.youtube.com/watch?v=s1ZNYqcaE1M
Or madman across the water:
http://www.allmusic.com/album/madman-across-the-water-mw0000190515
Or tumble weed connection:
http://www.allmusic.com/album/tumbleweed-connection-mw0000650322
For goodbye yellow brick road they did a drawing of Elton with a full head of hair:
http://www.walmart.com/ip/37869140?...88309288&wl4=&wl5=pla&wl6=89023729488&veh=sem
For rock of the westies they put him under a hat:
http://www.amazon.com/Elton-John-Rock-The-Westies/dp/B000001EM3
In Captain Fantastic and the Brown Dirt Cowboy they made a drawing of him and put him under a hat:
https://www.google.com/webhp?source...tXMUqnWSUXpSaW5BdZgaWKrcD6yoqqTAwBohq_pFIAAAA
As far as Billie Joe goes not only was he well established after he lost a bunch of hair but once he put out Piano Man he had a good shot of sticking because the industry found out how good he is. In the middle of his career he still had a bunch of his hair as evinced by the glass houses disc and the stranger:
http://www.amazon.com/Glass-Houses-Billy-Joel/dp/B00000DDMH
http://www.amazon.com/gp/product/B0..._m=ATVPDKIKX0DER&pf_rd_r=1819EYY79E6DEK5V9S2V
Ed Sheeran isn't even a big name and never was cuz I've never heard of him. Same for Michael Stripe and Ne-yo, whoever they are.
James Taylor had a bunch of hair a long way into his career.
When Phil Collins got in he had a bunch of hair and he built up a fan base with Genesis. He was the most talented member of Genesis.
Once a musician gets into the industry with some hits the industry is going to let him keep producing because they never know if he might come up with another hit. But getting into the industry missing hair is another matter. There may be a few musicians who got in missing hair but not many. Bobby Darin wore a piece and so did Sinatra.