In this instance, they met at a wedding. Danced. Had a conversation for sounds like an hour or more.
If that was me, I would have already invited her (if I was into it) right at that moment, and said I'll follow up with you. And then if you get ghosted or get the run around, you can just at least know you sent a good faith invite.
but, texting and texting about nothing, both parties trying to reassure themselves of whatever insecurity, only to be left hanging, is not a great feeling, and also highly inefficient. You can always get rejected, but put your shot up. This dude still never even got an answer, he got sidetracked in texts and lost his nerve.