I don't know what experience you draw from, and what is lost in assumption here (on both sides, "hard problems" is open to a lot of interpretation), but the entire premise behind agile is, that thinking a solution up is not how software development works. You chunk things up, you iterate, you stay flexible, precisely because sitting down and thinking hard is not realistically working for a sizeable, messy, real world business solution.
I draw from my 17 years of experience in the field, but I am well aware that people work differently.
There are the John Carmack types, whose output depends on how much time on they spend at keyboard, and the Rich Hickey types, whose output depend on how much time they spend on a hammock with their eyes closed (or under the shower in my case). I am afraid I am of the latter type. My best solutions are found away from the keyboard, as I have learned to simply depend on my subconscious to process and digest them while I'm doing other things.
Check out that talk still, it has deep insight on how the human brain operates.
