As somebody who long ago did print design, I totally get why designers would want pixel-perfect control. It is awesome, but you get that in print because you are physically manufacturing an object and sending it to people. The web was device independent from the get-go. It wasn't your paper anymore; it was their screens. There were a couple of designers I came close to beating to death with their own Pantone books because they refused to get that.
Sadly, the desire for pixel perfection led to trying to force every single user on the planet to conform to the designers' weaknesses and fetish for control. For example, every Flash intro in the world. Or all of the goddamn fixed-width "experiences" that were either too wide for what users wanted their window to be or so narrow that acres of space were wasted. An approach that surely looked fine in presentation to executives, but much less well for actual users.
The great improvements in CSS have definitely helped. But I think the major changes have been the the explosion of form factors (small laptops, giant desktop monitors, tablets, phones) and the rise of a generation of designers for whom the web is a native medium. The old paradigm got harder to force at the same time there were plenty of people who were thinking in a new way.
Planck wrote, "A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it." Design, like science, proceeds one funeral at a time. So goodbye, PSD2HTML, and let's quietly put a stake through its heart so it never returns.