On my own client (which isn't ready yet) the private key is entered like a password.
It's only stored locally, of course, but, at least from Google Chrome, you can save it like a password. Even though I don't have a "username" field, the browser even lets you set a username for that "password".
If you are syncing passwords between devices, your private key will be synced just the same way as every other password.
And even though my client doesn't allow you to use multiple accounts at once, your browser will let you save as many "passwords" (private keys) as you want, under different usernames.
Currently I test with two accounts: an account just for testing and this account right here, with different usernames, saving each private key as a "password".