> "Picking up the tab means I’m not interested. I want to feel like a princess"
Well I like your honesty. You know what you want, and you say it outright. Not using lame excuses like many women do.
Personally, a woman expecting to to be paid for when we don't even know each other, means I am the one not interested in her. It feels like leeching or, at least, entitlement; both are no-no in my books.
I look for a relationships where we support each other on an equal way. A balance of power, a dance where no one prevails. So sharing from the beginning signals that to me.
In the end, this attitude (both yours and mine) looks like natural selection: we discard the people who do not align with our desires and values. It works for me. :-)
But, as someone else said in the comments, the man paying doesn't mean he's leading: it means he is providing. I hope you notice the difference.