For years and years I thought that was how this worked. That you said you wanted to round up, and all of the money collected went into a pool that the company then used as a tax write off in one lump sum. So they were stealing your tax write off basically.

Nope, that's not actually how it works in the US (can't speak for other counties). If you round up your transaction for charity, you're eligible to write it off on your taxes as charity. Do most people? Nope. But could they? Yes! And some people even do save their receipts for this purpose.

The company doesn't get to write it off as their donation, because it's not. For them it's pretty neutral, they're receiving funds and transferring them on behalf of the people who donated them.

Note: I can't speak for companies that do donations for nonprofits related to them. I assume it's still neutral for them, since you definitely still can use it as your own tax write off, but I haven't looked into that side.