One thing that is changing quite rapidly in the field of web development is the breadth of devices you're aiming a site towards.
Back in the day you'd be fine with a fixed width design (say, 1024x768) that worked in IE, and maybe in Firefox.
Then, smartphones started getting more and more capable of being a primary browsing device for many users this has changed, and you were looking at two designs, one for mobile, one for desktop. (many sites used, and still use, the m. or mobile. subdomain to host mobile-specific sites, and for a time this was perfectly acceptable)
More recently, tablets became fairly common devices, and smartphones are being an even greater percentage share of the devices used for web browsing. This means two things; one is that we have at least one more layout to design (tablet, which is basically a mobile-style site with a browser-sized layout), the other is that users are expecting more and more functionality out of their mobile browsing experience.
Mobile-first is a design paradigm that allows designers to concentrate on the key UI and UX areas of a site for the mobile device, then add secondary functionality or design elements for the desktop site. This is basically a form of progressive enhancement where the desktop site is treated as the mobile site + 1.
Responsive design takes this switch to mobile-first even further. It allows the designer to have multiple designs, each with the same (or very similar) functionality, and adjust them to the size, and possibly input-method, of a wide range of devices without having to consider each possible size separately. This saves huge amounts of work from an implementation standpoint, but still lets the designer take advantage of the different purposes and sizes of devices to display information and functionality in the optimal way for each device.
Put simply, the changing face of the browsing market is why Responsive Design is gaining so much traction, and being talked about so much. And, like Agile, MVC, or any other "trendy" tech, we all know that the popular approaches and technologies tend to attract a large amount of wannabes and marketing nonsense. I'd also point out that neither mobile-first nor responsive design have a primary aim of increasing site speed, they're focused around increasing user experience on non-desktop devices, and speed is only a part of that.
I'd say that any highly-skilled, enthusiastic, designer is going to be looking to add Responsive Design to their portfolio of skills, in the same way that any responsible designer has already conquered Photoshop and CSS. Responsive Design is very much becoming less of a "badge" and more of a "must-have".
As for how to go about doing mobile optimisation? That's a big bag of tricks, but you're right about minimising the payload. Cut out as much HTML, JS, and CSS as you can for your mobile device version, and bring in additional content as needed for the devices on a proper net connection. At the end of the day, front-end optimisation is only one part of site optimisation; if your site is very slow to load in the first place, or badly written (such as in your ViewState example) you're not going to get very far with your optimisation by focusing on the HTML payload!