Dry hopping gives you a "bright" character to the aroma that late hopping will not give you. As others have said, how fast the dry hop character fades is hard to predict and control, but I've never heard anyone say that fact makes it not worth the trouble. As a stylistic nitpick, dry hopping is part of the distinct character if IPA, regardless of whether it's British or American, so I'd say if you're making a different style if you switch the hops from dry to late.
BTW, you can dry hop in your primary - just drop your hops in. Either loose or in a hop bag. If you use a hop bag, make sure they're loose, not packed tightly, and remember they will swell when they absorb beer.