Every time I use my iPhone to browse to Twitter or LinkedIn I'm taken away from the full site and to a silly "mobile" site that resembles the native app. If I wanted the native app. experience, I'd download and use it! Ever try approving a LinkedIn recommendation using your iPhone? Good luck!
It seems to me that many people think that "mobile responsiveness" is such a great thing, but I'm not sure they've really considered whether it's even necessary. I'd bet that most designers who build WP sites on themes that tout "mobile responsiveness" (and have it enabled by default) haven't even considered whether their client needs the second version of their site. Even if they do, I think often times the "mobile" version ends up being an ugly, hardly-tested, bastardized version of the "full site". Just give us the real website, please!