Many contra dances have tried a "first-time free" policy, but I think "second-time free" is usually a better choice. Most first-timers show up expecting to pay something, so you might as well take their money. Many first-timers don't end up coming back, so better to reserve your incentive for the ones that do. And it filters out people who are only interested in free experiences. BIDA switched in 2022 and I think this has gone very well.
I think the main case where first-time free would be a better fit is a community where you're having a lot of trouble getting people to come out and try the dance but you're pretty sure that if they do they'll stick around. But while contra can be pretty addictive I don't think it's that addictive.
(This isn't something we came up with; for example, here's Tucson in 2008.)
Good call! I have a use for this idea :)