Bad idea.

I leave my browser on and go study/work during banish events.

And banish events represent a significant chunk of income for all players.

That said, I'm sure some servers/realms are having difficulties killing their bosses as some of their players are too busy to play, while a few lucky ones can just leave their browser on to help chip in for the boss fights.

If anyone wants to optimise their damage output during boss fights, I would suggest they constantly refresh their browsers once they get into each round of battle during Cerb/Baal.

Why punish players who are not being able to be at their PCs but still willing to help out in boss fights?

I think the developers should concentrate on adding useful functions, instead of removing them.