How would you sending .00001 BTC prove you sent the initial 0.01 BTC? It wouldn't.
People don't sign transactions, wallets do - and there is no reason one should ever assume there is a 1:1 relation between people and wallets.
The users of air conditioning don't know how air compressors work.
The users of airplanes don't know how the navigational computers work.
The users of cows don't know how their DNA works.
Why should the users of Bitcoin be expected to know how its scripting works?
"How would you sending .00001 BTC prove you sent the initial 0.01 BTC? It wouldn't." If I can send from the wallet I am the owner. Am I missing something? if you can send from the wallet you are the owner of that wallet. I mean shit
Also, wallets may have many users, not just a single owner.