The same could be said about all the humanities. But how do you know ideas don't bubble to the surface collectively as a result of competition between ideas throughout the culture? Geniuses interact with the culture, and without that familiarity they'd be crackpots.
Scientific problems may be more numerous, but they're not as fundamental or as subjectively important as the philosophical ones. Science tells us how things work, while philosophy and the arts tell us what we should do.
It's also scientistic to compare philosophy to science, as though philosophers have "problems to solve" or "products" to sell. To be sure, the discipline's professionalization has engendered that scientism, but it's still misleading.