Wolverine is too much of a loose canon to be a good bodyguard. I think he's occasionally done that work, but it mostly ends in tragedy. He doesn't get a lot of happy endings because us authors are cruel, cruel beings, so his record for keeping people alive doesn't look good. Most of the other "good guys" don't kill their opponents.

Since immortals are so thoroughly in the gray zone between good and evil--they're all serial killers but it's always and serially self-defense?--it's probably hard to get loyal bodyguards. Easier to just protect yourself than to trust an armed person at your back.