They could just have, you know, used a bigger cart like Mistwalker did for ASH, a game that's also filled with voice acting and FMVs, on the DS. Sure, would be more expensive for the gamers to buy, but FF IV is a fan favorite in Japan, people will buy it anyway, regardless of the price.
If they are only are going to do one FMV then I would prefer no FMV at all. It gives the player wrong expectations. I would have loved some FMVs in FF III DS, and I knwo some occasions where it would greatly help the game. But instead we got a beautiful but still pretty useless intro FMV. FF IV DS is a highly story driven game and by the looks of the entire game, it's going as far as rival FF VIII and IX IMHO. In-game FMVs would be a really welcome thing and make me fondly remember the first time I played FF IX, my first 3D FF and also the first 3D RPG and Playstation game I ever played, albeit on my PC with ePSXe 1.5.2
I'll never forget that moment with that beautiful opening FMV of FF IX. Having something likewise on my DS but with FF IV would be a moment just as memorable. Instead, we get another beautiful but useless intro FMV that makes all those great CGI versions of the characters go to waste. Bad move, SE. At least the directors of Revenant Wings knew better.