Say the user has two devices and hence two copies of the same passkey, let's call them A and B. They have a shared signCount.
Say an attacker manages to make a copy C of A. They have the signCount as part of it, right? So they can immediately connect to the server. The server will increment signCount and sync it with A and B, but C is already in and C knows that the signCount is probably lastSignCount+1.
The only way I could imagine signCount to be useful is if somehow the server synchronises it between A and B in a way that C - who got access for a while - cannot access. It would mean that C has access until A or B connects, and after that the next time C connects, it will be out of sync. This does not sound super useful, and it assumes that C cannot access the sync process even though it has unlimited access to the passkey (until A or B is used).
What am I missing? To me signCount doesn't bring anything here...