It seems to me that philosophy is most important for refining mere intuitions and bumbling around until we find a rigorous way of posing the questions that are associated with those intuitions. Once you have a well posed question, any old scientist can answer it.
But, philosophy is necessary to turn the undifferentiated mass of unprocessed data and potential ideas into something that is succeptible to being examined.
Rationality is all fine and good, but reason applies known facts and axioms with accepted logical relationships to reach conclusions.
The importance of hypothesis generation is much underappreciated by scientists, but critical to the enterprise, and to generate a hypothesis, one needs intuition as much as reason.
Genius, meanwhile, comes from being able to intuitively generate a hypothesis the nobody else would, breaking the mold of others intuitions, and building new conceptual structures from which to generate novel intuitive hypothesises and eventually to formulate the conceptual structure well enough that it can be turned over to the rationalists.
“3. Philosophy has grown into an abnormally backward-looking discipline.”
Indeed. One of the salutory roles that philosophy served until about the 18th century (think e.g. “natural philosophy”) was to serve as an intellectual context within new disciplines could emerge and new problems could be formulated into coherent complexes of issues that became their own academic disciplines.
In a world where cosmology and quantum physics and neuroscience and statistics and scientific research methods and psychology and “law and whatever” are vibrant we don’t need philosophers to deal with metaphysics and epistomology, but we may need considerable more philosophical attention to questions like “what about a book has value?”, or “what obligations do people have to each other in an unequal society?,” or “what does it mean to be human?”
One of philosophy’s main cutting edge agendas should be formulating new questions to ask and serving as an incubator from which to outline the boundaries of new disciplines of specialists to answer those questions.
Any summary of the discipline that is looks like an index of the last two thousand years of philosophical thought is probably missing the stuff that philosophers should be spending their time considering.
Alternately, one approach that many academic philosophers seem to be fond of taking is to consider themselves to be primarily intelllectual historians, with a particularly rich and subtle tradition to understand so that it can be understood by those who are primarily interested in the history of ideas. In the same way, Freud is a bad place to look for someone interesting in doing clinical psychology, but a good place to look for someone interesting in understanding the conceptual roots of lots of ideas that shaped by lay and professional understanding of the individual mind.