You can file a case that the exchange has stolen 100 BTC but there is no way they could prove the BTC belonged to them without a KYC.
You can prove BTC belong to you signing a message with your BTC address.
Exchange can prove owning their address signing a message with that BTC address.
You can prove depositing BTC to exchange address pointing transaction id on blockchain.
KYC does not prove anything. It is an image uploaded to one exchange then stolen and uploaded by somebody else to another exchange then stolen and uploaded by somebody else to another exchange.
Bitcoin is proof of ownership and change of ownership.