I think it's primarily the solo aspect of flying that makes such a difference
Yup, me too.
Being sent solo in an aircraft is a demonstration of trust that you can handle it. The owner is satisfied that you have what it takes - now you have to fill those shoes. A pilot who has never been sent solo never really knows that they are trusted, nor have demonstrated that level of skill - someone else is still there to hold their hand. For years I bimbled about solo as a student helicopter pilot. I could take the helicopter here or there for lunch or whatever, as a solo student, with my instructor's signoff. I built decision making skills for helicopter flying, in a different circuit (really none) and quarter of the same airports I knew well as a fixed wing pilots. Then, I earned my helicopter license (really to enable acceptance of the offer of a type rating on a bigger machine). But with that, I lost the status of "student" and was no longer able to take a machine solo. I have not flown one solo since. Not for inability, but for reasons of insurance. So I'm baby sat when I fly helicopters, with a more experienced pilot who tells me I fly fine, but I never really get to prove it to myself, nor make little mistakes from which to learn, as he will "suggest" a better way before I find that my idea was inadequate.
Solo flying just builds vital confidence.
Though aerobatic and taildragger is not critically important, that type of flying will always make a better pilot than not. Either will demand that the pilot control the aircraft with precision that no other fixed wing flying will require. Once either or both of those flying types are somewhat mastered, the pilot will be much more able to sense any small deviations from the intended flight path, and instinctively return the aircraft to the intended path with much less delay, or oscillation about the intended path. Simply, they won't be sloppy any more, and they'll remember that the rest of their career.