Besides its undying association with one particular performer, "Funny Girl" also suffers from being a star vehicle with no mainstream performers talented enough to pull off the role (no one able to bring in major audiences, anyway.)
Realistically, no one other than informed members of the theatrical community (who are minorities in the grand scheme of things) would be interested in going to see Murney, Block, Kritzer, or anyone else of their stature take on Fanny Brice (though all are qualified to do it, some more so than others.)
The show itself does not have a built in enough fan base to work without a major star. Casting a phenomenal nobody in the lead role worked decades ago because no one had heard anything about the show, but the majority of it's loyal followers now are as passionate as they are about the show because of Streisand, and without her, many of them would probably not be interested.
The only place I could see this working is as a limited engagement through an organization like Roundabout, but even the odds of that happening are extremely slim.
Tonya Pinkins: Then we had a "Lot's Wife" last June that was my personal favorite. I'm still trying to get them to let me sing it at some performance where we get to sing an excerpt that's gone.
Tony Kushner: You can sing it at my funeral.