There may be a couple of reasons: First, Tim's family would most likely look down on them for accepting money that way and not earning it. And second, Tim wants to be "the man who takes care of the family" with no help.I'm surprised they don't have patreon or do superchats. I imagine patreon would be too much work for them and they would never deliver on the tier promises anyway. Maybe accepting donations is below them now, who knows. I just don't understand how they have enough money to blow it like they do.
Paetron was created in support of artists. Tim is nothing of the such, although there are Disney vloggers out there who are (Justin Scarred, Mr CheezyPop, etc)