It's red meat to the base. DeSantis is running for president, and he's promising to 'make America Florida.' I think he understands that hardcore conservative Republicans want anti-LGBTQ animosity to center on the political stage in 2024.
Also, it's important to know that, unlike Trump, DeSantis really is a committed fundamentalist Christian — with all that says about evangelizing and forcing beliefs and practices on others.
Given his religious tradition, he grew up inculcated with the idea that Christians in the US are persecuted. So, in some way or another, he probably believes this bill is necessary to counter persecution.
Or if he doesn't, most of his strongest supporters do, and he'll be giving them what they want.
Part of what makes DeSantis so much more dangerous than Trump is that DeSantis actually has values, albeit values that many Americans find abhorrent.