Let’s look at this from a different angle. Instead of tzedaka, let’s talk tuition collectors.
They’ve got a real nasty rap. Nobody likes them. At least not in the parent body! But you know who loves ’em? The rebbes and teachers that wouldn’t have food to put on their table without the tuition collector bully chasing down the parents…
Yes, there is overhead when it comes to tzedaka. But think of the rebbes and teachers- that overhead is going to feed their kids. These are people we are talking about!
A chesed organization cannot run soley on volunteers round the clock. Every organization needs some kind of paid workers, in order that they CAN devote their time to helping the organization.
A volunteer who has no money can only volunteer for the time it takes to starve…
So, yes, feel good when you give to tzedaka, knowing that even the “overhead” keeps the chesed going!