Paswordless public key-based SSH login on router with Asus Merlin firmware
Solution 1:
Put your public key in /etc/dropbear/authorized_keys
edit:
I originally thought dropbear was not reading ~/.ssh even though it should, so i pointed the default directory /etc/dropbear/. authorized_keys is not there by default so it isn't so obvious.
rereading the question i realized you were confusing host keypairs with login keypairs.
you need to accept the routers host keypair (/etc/dropbear/dropbear_rsa_host_key) and place your public key on the router in either location' authorized_keys file and you should be good to go.