Responsive web designs are not magic bullets
At the risk of "teaching Grandma to suck eggs", it's worth re-stating that a responsive HTML5 and CSS3 web design is not a "magic bullet" panacea for all design and content serving challenges. As ever with web design, the specifics of a project (namely budget, target demographic, and purpose) should dictate the implementation. However, in my experience, if the budget is limited and/or the programming of an entirely bespoke "mobile website" isn't a viable option, a responsive web design almost always provides a better and more inclusive user experience than a standard, fixed-width design.