The answer is that it's much simpler to send everyone a check. The rich person will pay more in taxes than the amount of their check, so it doesn't matter. Indeed, the arguments that we should do otherwise are to the benefit of the rich, because the proposed cutoff invariably comes somewhere in the middle income range, resulting in higher marginal rates on middle income people rather than higher income people.
In other words, a cutoff allows the rich to pay lower taxes in the amount of the money that had been going to people in the middle.