I think it depends on your threat model, how you use your devices, what services you need to use, and some other details. Personally I would not enter my passwords on someone else's device (a stranger on the street?), so I would not do what you suggested in case my phone was stolen. I'd just hope my screen lock prevented the thief from accessing anything, at least until I got home on my computer to track or lock the device. If my screen was not locked, well, uhm, let's say my mitigation of this threat is still in progress.
Anyway, here's a list of passwords that I think should be remembered in general:
- Password for the password manager (master password)
- Password for full disk encryption of your computer
- Passwords for full disk encryption of your backups (external HDDs, USB sticks, etc.)
- Password for logging in or unlocking the screen of your computer
- Password to unlock the screen of your phone
- Passwords to access the most important services (at least your main email account from which you could reset the passwords of most of the other services)
Note that most of the above passwords won't be difficult to remember, because you are forced to use them every day (to unlock the phone, boot your computer, etc). Also, if you use an online password manager, you don't really need to worry about remembering the passwords for your backups, because if your computer blows up you can always log in to your password manager from anywhere and retrieve the passwords. But in my case, since I use a local password manager, if my computer blows up I'll have to rely on my backups and be able to access them.
So as you can see, it depends. If your threat model requires you to be able to access a certain service quickly without using your password manager, then yes, consider learning that password (or change it to a passphrase you can learn and remember more easily).