I need to research more about tau, BUT does proof of transaction means that if an wallet X send Y coins to another wallet, Y stakes will be added to wallet X?

This could lead to problems like guy sending coins from wallet X to wallet Z and then from wallet Z to wallet X and then from wallet X to wallet Z and this goes on and on and on.... You problably tried to make some changes to stop this and other problems, but my question is:

Why not just make it proof of transactions fees, instead of proof of transactions? Its very close to proof of transaction and solves alot of problems.