You never really mean pixel, so I guess you're arguing for the removal of the px unit completely. (bzbarsky explained this better: http://news.ycombinator.com/item?id=3697227 ) Then designers would start asking for a unit that is resolution-independent but always an integer multiple of pixels — essentially px under a different name. The px unit is really useful, but maybe it should have had a different name; it's too late to argue about it now.
On the rare occasions where I say "px" rather than some scalable unit, I really do mean pixel. For example, I might use px to specify the width of an element that needs to have exactly the same width as an img tag.
On devices where 1px != 1 device pixel, images should be scaled by the same proportion as the px unit. So, if you set an img to 150px wide, and a div below it to 150px wide, they will be the same width, even if 150px == 300 pixels. I'd be happy to learn of any browsers where that is not the case.
HTML is a text markup language, not a device interface language. CSS is a page layout language. HTML and CSS are designed for optimum user control as well as designer flexibility. You assume you're designing for one type of device. Designers before you have assumed 96dpi for web pages. The W3C realize these assumptions, realize that the user may want to use a different type of device, and thus define px in terms of DPI.
As others have mentioned, if a user prints a web page on a 1200dpi printer, your 960px fixed layout is 4/5ths of an inch wide. Your users would not be pleased. Under the device-centric interpretation of px, you'd have to provide a medium-specific style sheet for every possible type of output device. Designers would not be pleased.
Maybe you're trying to use HTML+CSS as a rendering target for a general purpose widget library like Gtk+. In that case, I can understand your frustration.
