Yes, the transfer agent can ask for a key signing before moving funds, but they also need to be able to transfer WITHOUT the key. Examples would be a key loss or transfer of ownership due to court order. I don't know what the key is doing since it's optional and highly fallible proof of transfer intent.

At best the key signing is providing a partial audit trail with no case law to support any liability transfer created by its use. Typically transfer agents take very little liability by requiring a medallion signature before allowing a transfer.