The German Idealists would argue that ignoring the connection between problems is the real intellectual failure.
From their perspective, the "problem-solving" approach of analytic philosophy is like trying to fix a single gear in a machine without understanding how it fits into the entire mechanism. They'd say that a solution to an isolated problem is only a true solution if it coheres with all other truths. If a philosophical claim about free will doesn't fit with a claim about the nature of time, then one or both of those claims must be flawed, and the point of philosophy is to find a new claim that resolves the contradiction.
For the Idealist, the very act of philosophizing presupposes the existence of an underlying system. They believe that if reality is intelligible, it must ultimately be a coherent whole. To give up on the idea of a complete system is to give up on the very project of philosophy itself—the search for comprehensive truth.
This is where the accusation of "intellectual cowardice" comes from. In this view, analytic philosophers are not being more rigorous; they are simply refusing to do the hardest part of the work. They are settling for "truths" that are true only in a narrow context, rather than pushing their intellects to the limit to find truths that hold universally.