I would assume almost all daily users of Wordle would consider having to have an account in exchange for persistent, cross-device statistics a worthy trade-off. And presumably a well-designed app could even abuse LocalStorage for anonymous play, and include a mechanism to hand off and save your data, should you wish to, via a login.

Social OAuth and passwordless email login (essentially one-time codes) are both pretty low-effort ways of managing auth without storing a lot of sensitive data or having to manage passwords.