The view count does convey useful information. For example, if the view count is low then this may be because the questioner chose a poor title. Knowing such, the questioner can revise the title to help the question get better exposure. If revising the title doesn't help raise the view count, then this may imply that not many members have interest or expertise in the matter, so the OP may wish to look elsewhere for answers (e.g. MO). And if we know that we don't have much expertise in certain fields, we can use this knowledge when recruiting colleagues to help fill gaps in community knowledge. When new experts join, and they browse the list of unanswered questions, they can use the view count to help infer which answers would be of most interest to the community.
By the way, does anyone know if the view count is the count of users who viewed the question, or does it (sometimes) count multiple views by the same user? This is useful to know to help assess if anyone has viewed a (relatively late) answer, or an answer to an old question. If the view count is just a user count then it is not very useful for such. Otherwise, view counts can relay useful statistics to answerers. For example, if my answer received few votes then this may be explained by the fact that there were few views because I posted it too late. But if there were many views since I posted my answer, then there are probably other reasons why it didn't get many votes (probably too general!) Thus, armed with that knowledge, I can attempt to improve the answer, so that it is accessible at the level of the majority of readers. Sometimes I will explicitly keep a page open to my answer so that I can easily track the number of votes per (new) views, to help gauge how well the answer was received.
Similarly one can make other statistical inferences based on view counts that may help to improve the site. I encourage others to mention ways that they've devised to use the view count to help improve the site. This could prove very useful to new members.