What about Blackrock? Their representatives sit on many boards in a single industry. Same with large VCs. It's not as structured as unions, but each board is not a completely independent entity either.
This is actually a good point, and is detrimental for similar reasons: concentration of power, reduction of competition and increased fragility of the whole system ("too big to fail").
Well, i have something you might want to hear about. It's called investment funds and weirdly competition between companies started to fall as investment fund rose up. They also are present at a lot of different director board or committees.
Yes, board members are strictly segmented by business sector, by law. I mean, god forbid we could have someone on the board on an aerospace company, a car manufacturer, and an internet behemoth! /s