The implicit advocation here is "design for the least common denominator". That means no hovers, no gestures, no secondary/tertiary clicks, no modified clicks, no long-presses, no multitouch, and big fat click targets that allow for lots of slop. That's all well and good until you realize that this leads to designs which are wildly inefficient on certain classes of devices and drive users away because the information density sucks and the interaction models are stunted. If you can get away with it without damaging your UX, then by all means, go for it. Device-agnostic design is awesome, but it's myopic to damage the UX for the vast majority of your userbase because someone might access your website on their XBox and use their Kinect to navigate it.
Know your audience and design appropriately. You're never going to design a perfectly futureproof website; make sure that your users today and tomorrow have a great experience, and then just keep iterating on that.