Good points. There are also finite resources, so I'm sure bishops have to carefully weigh who gets helped by the donations, and to what extent. Someone who has, for example, faithfully paid tithing and other donations but has fallen on hard times may (I imagine) get a higher priority than someone who has never done that. Or maybe not, if the second individual/family is deemed to have a higher need. I'm certain the bishops in the church have many tough decisions to make.
From the bishops I have known this is governed by their personal opinion (first and foremost), some direction from the stake, and guidelines from the brethren.
My dad always tried to help who he could and put their individual needs ahead of their status in the church. If you needed more than someone else, you got more.
By brother-in-law (currently serving as a bishop) is very stingy (by his own admission) and he has a generally bad attitude about people in need, leaning toward the idea that they are just looking for a hand-out and are generally lazy. He says some of this is driven by the stake to be better stewards over funds, but that is his cover imo, it is really his own attitude. Which is weird because in general he tends to be very liberal for a mormon.
Another bishop we dealt with, when we had a health crisis early in our marriage before I started into my career, insisted on checking our cupboards (literally) and bank accounts and bills before issuing even a bishop's storehouse order, and even then he let the RS president fill it out, then he cut items off the list. He made us feel like we were criminals that needed to be kept in check. He claimed it was because so many people take advantage. It didn't matter than before I got sick we had given freely, even taking on a sub-for-santa family one year when our kids were little and we had a little extra money. As soon as we were in need, we needed to be kept in check so we didn't "take advantage", whatever the hell that means when he decides a family of 5 with small children need 1 instead of 2 gallons of milk for the next 2 weeks, and don't need any carrots or apples (yes he cut those from our order entirely). But he left the canned beans on there, all 6 cans, so we ate a lot of those.
In short I guess the church just puts these guys in place and lets them run things the way they see fit. They are human beings and will all have different takes on how to handle their stewardship. And frankly, some will be better stewards, of both the flock and the money, than others.