Even though I imagine management to be way harder and more time consuming in times without computers and other tools, this is still bullshit. Even "poor" people have to run their (or their bosses) workshops, kitchens, stalls/pushcarts/shops, work the fields or have to beg as long as possible to make due. Investing and squandering time is therefore very costly in its own way. If you do it in your free time, it's only an illusion it does not cost you anything. You cut at your health and lifetime. Those rich guys buy something very precious and it is a real bargain.
See it the other way around. If you let them stand in the waiting line with the rest, they might not be giving that much (or any) money, but maybe they will pressure the local government to do something about the bad situation. Waiting is boring afterall. And seeing all those other people and talking with them might hurt their picture of the world. This is also yucky. Right now they simply don't really care. Make them care. We'll see if a betterment of the situation isn't worth the cut in donations.
Also don't tell me about how they have to take care of their companies or whatever, that employ many people and/or deliver important goods and services needed for society (huge responsibilities) and it is taking up their time. Yet again BS. Their management should be good enough to leave them enough time or they at least should have trained people to step in in times they are sick for example. Even if there are enemies of them, that are waiting at the sidelines, this is no excuse, as other things might also occupy them. And those things are also true to a certain degree for poor people. They also have children, elder parents, family overall, co-workers (that count on them), animals to take care of and adversaries to also take care of. No excuses.
I know the argument of morals vs. compromises, that are hurting morals, but are necessary to make things work out...But most religions are build on morals, aren't they? A religion, that ignores its own morals, hurts itself. Badly. Even the worse, if there are alternative approaches (see above) to those dirty compromises.