re: What popular bands still tour with little or no original members?

There are some crazy stories, especially involving managers.

The Vogues ("You're the One", 1965) were sued by their manager who owned the name. In a settlement they were given the rights to play their hometown Pittsburgh area. He got the rights for everywhere else.

Moby Grape's manager would not advance them money unless he owned the rights to the name. For 50 yrs he would not allow them to use it. I think they played one reunion show as "Maybe Grope". I believe they finally got the rights back about five yrs ago.

The king of this was probably the Drifters' manager, who kept a revolving door on members (& paid them as little as possible).

But perhaps the strangest story involves The Zombies ("She's Not There"). For many yrs there apparently was a band using that name, touring the state fair and small time oldies circuit, totally unbeknownst to the actual band members & rights holders, & certainly w/o their permission.