It could work for a select group. The reason why other donation models are successful is because they offer something (insider access/game earlier) that makes you feel special without the badge.
This is something else I've been thinking about! Caleb Porzio's post from last month describes a Patreon-style
"insider access" service built on top of GitHub Sponsors. I think it's a phenomenal idea. Ideally GitHub would also implement something like that "natively" as part of the Sponsors program.