Answering my own question here based on an idea I had just now.
RP Pico W has Bluetooth which allows for requesting the WiFi password wirelessly from a device in a more secure location. Examples of secure locations being a nearby server in a locked room, or a phone in your pocket.
"How is this any better" you may ask.
To acquire the password an attacker need not only have physical access to the Pico board itself to get the BT pin, but also be within BT range to request the pin, and the server sending the pin must accept the request. If server requests are acknowledged by user after verifying device integrity, i.e. no signs of any attacker, an attacker would need to put much more effort into getting the password compared to just reading device memory.
Normally requests should only ever be sent after a power outage or other cause for board reset. Operating effort should be minimal.
Additionally, having device unique BT pins means only compromised devices needs to be flashed with a new BT pin.
Overall I think above strategy should make an attack much less attractive to perform due to the additional effort, and much more risky as it must be performed on-site with the owner nearby, while not adding to much to operational effort or programming complexity.