My bank currently reprompts me for password whenever I make an important transaction (e.g., transferring out lots of $$$, or adding an account). Should they drop that security feature when they switch to passkeys?
Yes, because it's both annoying, and adds no extra security if you're using a password manager. While the database is unlocked, the password is in memory, and reprompting the user to enter in the unlock code for an unlocked database is just security theatre.
This assumes the attacker has unrestricted access to memory. If a malicious actor has that level of access, you've already lost all security guarantees, regardless of the auth mechanism.
A more realistic scenario is where the user has installed a malicious extension that can exfiltrate the cookies. Requiring reauthentication makes an exfiltrated cookie less valuable. While the extra auth step can be annoying, it also provides an opportunity for additional safety checks (like validating that the IP of a request matches that of the recent auth).