My dd's dance studio runs like everyone else's - you pay monthly, but get a discount if you pay for the full year up front.
The only reason I could think of for this studio's new policy (having taught gymnastics at a dance studio) is that because many kids drop out of activities so abruptly, they may end up with a class that's too small to make a profit. The new policy may be the equivalent of holding a spot in the class. Still, I think it's risky for the owner to do this because she'll probably lose people who don't want to pay up front.
I'm not saying my theory is right, that's just my guess. I understand and agree with your skepticism on this.
As far as the cost of dance, I tell anyone who's interested to just double the monthly tuition cost because that's how much you'll pay in the end (at least). But I have to say, my 4 year old was in her first recidal this past year and enjoyed it so much!
Good luck with your decision.
Allison