I've seen that argument while reading up on the current state supreme court cases, but I disagree that it's more like searching your mind than searching ahouse is. To mirror your examples, a house may have handwritten notes, photos, and voicemail messages (well, if it still has a landline) all of which can potentially contain incriminating evidence. Yet we compel people to grant entry to an officer with a search warrant.

As to the protection afforded by a password, a house is protected with a lock and ordinarily someone cannot compel you to grant them access, which is what the warrant is for, stating that they have reason to believe there is evidence on the premises.

If we want to say, "But unlocking a door doesn't require speech while telling someone your password does" then fine, silently punch that password into the device.

Mainly I'm looking for problems with this in the vein of "If we install backdoors into our software, that compromises security for everyone and grants unprecedented surveillance power to the government". A hand-delivered court-issued warrant to the owner of an individual device seems like a promising compromise to let law enforcement get on with investigating specific crimes without broadly crippling everyone's security in the process.