The biggest reason for me to pass on implementing an approach like this is what I THINK is the actual most common use case for a typical user when logging into a site at which they are a regular:

They're doing so for the nth time, and on the (or a) device they usually use, and thus their browser (or other password manager) has already got their password remembered and thus it is pre-filled in.

Having to click back and forth between email every time you log in seems way clunky relative to that, which for me is something above 90% of the instances I log in to some web application.

Couple that smoothness with picking a non-reused, strong password for a web application (which password managers make actually practical) and the friction in the user login experience seems to have little if any upside.