Yes, your canister id matters for the key derivation, so simply reinstalling your canister on a different subnet while using threshold signatures is not going to work. Subnet splitting makes sure all canister ids are kept, so that this is not a problem. The protocol does not offer an easy way to transfer your canister without changing id yet, so this is a downside you have to consider if you manually move your canister. I hope we can address this limitation with future improvements.