Well that depends. If the display width is below 640px, I eliminate the heading and menu on all but the "home" pages. So the site does adopt a more linear approach, but all the information is still there. That includes my "Relativity Myths" site that deals with complex, anti-intuitive, ideas like how space and time combine to form a 4D spacetime continuum, and the meaning of zero spacetime intervals. Of course that does not answer the question of whether people would choose to view a site like that on a low-spec smartphone. I'm just saying that it can be done.
Furthermore, if I needed to use graphic images larger than 300px wide I would eliminate them on "handheld" devices because, in my experience, the alternative of dynamically down-sizing large graphics on small screen devices is a no-no. The download time is excessive, even when using a wifi hotspot instead of 3G. At least that is the case with the lo-spec smartphones I use for testing. I wonder whether people who advocate that practice have tested their sites under realistic conditions?
I'm investigating the use of separate graphics on high/low resolution devices, but so far I have not found a solution to the problem of BOTH graphics appearing on IE8 and below. That is THE major issue. I suspect that people who advocate that technique have either found a solution, or are not testing on IE8!