Am I missing something?
No, you're not missing anything. A $10 unfranked div and a $7 franked div are equivalent.
But that said, I prefer franked dividends because it means the business is paying tax, which means it's probably not just reporting imaginary profits and paying dividends out of borrowings or capital expansion. It's a useful 'sniff test'.
(But there are plenty of business that have a good reason for not paying fully franked dividends - notably those with offshore earnings. So some interpretation required).