How can philosophy make itself more relevant?

Truth is most academic philosophy is irredeemable garbage of the first order. Philosophy was transmitted from the Greek to the Latin, from the Germanic to the French, and presumably it was also extended to the English. There is in fact a clear line of descent in terms of the reasoning and discoveries made which can be traced from the Pre-Socratics to the critical romantic enlightenment strains of Kantian and Post-Hegelian philosophy, ending ultimately in a series of complex distortions wrought by the Marxist school.

After the second World War, however, a rupture occurred in the English language tradition that broke ties with this movement. This is why we have a "Continental" / "Analytic" divide. The former attempted to stay consistent with the philosophy passed down to the Germans and French, whereas the latter severed most of its relations to these systems of thought. It did this by largely cherry-picking the parts it liked from the Renaissance scientific thinkers along with certain Irish and British figures like Hobbes, Locke, and Mill but without ever confronting the Germanic philosophy at the peak of its development (the only notable exception being British idealism, which was shortly replaced by the logical positivists). Although it later made some amends with Kantianism, what the analytic tradition has ended up with is a one-sided formal empirical philosophy grounded more in ideological posturing than the rational discourses that characterized all preceding philosophy.

What people call British-American philosophy today then is dangerously out of step with itself. It's retracing the same errors that were worked out centuries earlier by their predecessors. There are countless examples of this, which I simply don't have the patience to enumerate. That's not to say the Continentals are without blame. They've created their own share of mistakes. But that, in effect, is a very large part of the answer about why philosophy is mostly irrelevant today in North-America. It was lead down a blind alley by ideologues and has yet to recover.