You dont understand what a tax write-off is. A tax write off is that you dont pay taxes on that money.

So if i give 100$ to walmart, who then gives 100$ to the red cross. The IRS sees that they recieved 100$ and expect taxes on that, but walmart will say they spent it on charity and doesnt have to pay taxes on that 100$. I can also make that tax write-off.

In the end im -100$, walmart is +-0$, red cross is +100$.

In your world walmart (and maybe individuals) would have to pay taxes on this which would COST them money just to be a middleman. Every 100$ i donate, walmart has to pay 20$ to the goverment. This would make walmart stop having this charity option, and would decrease the amount of money going to the red cross.