Yes web programming in C / C ++ is possible , this also refers to the start of dynamic web applications. In the '90s CGI with Perl for text manipulation and C / C ++ for "heavy processing" were the norm.
The programming language, on average, is not the first bottleneck of a website. Network latency, IO, etc. are factors that weigh much more than language in the vast majority of cases.
Of course the cost of processing exists, as well as the cost of scaling a website to handle thousands / millions of concurrent requests ... Also, with studies indicating that a one-second delay can impact sales by 7%, there is an economic incentive to optimize performance >.
You do not need to expose developers to the C / C ++ idiosyncrasies to get a significant performance gain. In fact, even assuming that a properly optimized C / C ++ solution will always be faster (which is not true), the law of diminishing returns makes extracting these last drops of language performance in a world with so many other factors unlikely to be worthwhile.
In the great majority of cases, it is not feasible to give up years and years of evolution of the languages, tools, techniques and knowledge accumulated by the various communities specialized in web development to write a solution in C / C ++. Frameworks for web development in C ++ such as CppCMS and Wt , regardless of technical merits, simply do not have the same traction of technologies in more recent ecosystems.
In this way, I would say web development in C / C ++ is possible and there are applications in certain niches. That being said, I see little chance of such development becoming mainstream . The argument of performance gain with C / C ++ to avoid crashes does not hold up, and it's hard to think of a good reason to write web applications in C / C ++ in 2016.