Nope. Android has this API where an app that is confirming your phone number with an SMS can automatically read it (without having access to the rest of your text messages) , but not all apps implement it (probably the majority though).

This is the type of feature Apple are capable of doing because they own the full stack - phone OS, computer OS, browser. Nobody else has that (well Google do with ChromeOS but i doubt such UX is a part of their focus there).

Of course the problem is that if you want to use a different browser, or Tim Cook forbid, a different mobile OS, you lose of all that because there's no interoperability. A form of vendor lock-in if you will.