You think it is a sad picture for the physical sciences, try and name any “public intellectual” from the biological sciences. It often seems that the only biologists of any repute are goofy television animal show hosts (aka Steve Irwin, RIP) who only had a high school level education and is currently dead, those who specialize in anthropomorphizing animals (aka Jane Goodall), or evolutionary biologists fond of spouting off controversial and ill supported philosophical musings (aka Richard Dawkins). Ask average Joe citizen to name any biologist alive today and I guarantee you will mostly get blank stares. The biological sciences sub-disciplines, which frankly are much more influential and important in the modern world (a highly controversial assertion I will grant), such as micro/molecular biology fare even worse.
In my view the biggest hurdle to scientists of any stripe participating in the public sphere is that by and large they are smart people. As such they realize that the upsides of participating in public discourse in an outspoken and visible way are so outweighed by the downsides that even if they were in a position in which they might do so, they choose not to. It is a simple risk-reward calculus that always gives the same answer, ultra high risk, very low reward. For the vast majority of scientists this is a no brainer. On the other hand, anything a vast majority of people are doing is something I try to avoid, so count me in as a volunteer. Public intellectual scientist here I come. Now I just need to figure out how to get famous. Maybe publishing little viewed and generally unhinged rantings on a mid grade web-site with almost no public visibility is just the ticket…maybe…lol!