Why does Mario have to collect 1,000,000 coins in the first place?
He doesn't. It's a completely optional goal.
That's a very loose use of "Completetely optional", seeing how most of the advertisment campain, and even the cover of the friggin' case says to collect 1,000,000 coins.
Why is the game called New Super Mario Bros. 2? Sure, it's the second handheld version but it's the third entry in the series overall. Besides, "New Super Mario Bros. 3" would make much more sense since, you know, it's on the freaking 3ds and the game clearly takes most of its inspiration from Super Mario Bros. 3!