I don't even have a smart phone, I assume there is some sort of fallback behavior?

The fallback is that you get redirected to a website helpfully demanding you buy a Google- or Apple-vetted smartphone: https://support.google.com/recaptcha/answer/16609652.

You will also see this page if your smartphone is degoogled and you try to open the reCAPTCHA attestation URL in a web browser instead of in Google Play Services.