Celebrim
Legend
This now seems to be a discussion of the merits of sandbox versus storytelling, more than a discussion of min-maxing.
I hope it doesn't go there, because I don't have a dog in that fight. I don't believe that there is just one way to be a good DM, and I move back and forth - sometimes in the same campaign - between more linear and more open ended scenarios. And I think that a player can enjoy campaigns equally with more character driven goals and with more DM driven plots. I do not think, "Well, I just run open ended sandboxes exclusively." is the answer to the question of what to do about narrow gates in the story/play. It is an answer, and it may work for you very well, but it is not the definitive answer.
And as long as we are talking about how the thread is potentially forking, it is a thread unto itself to deal with the complexities of handling the combination of player skill and character skill. Generally speaking, power gaming or Min/Maxing is assumed to be maximizing character skill, and not player skill. Cracking down on abuse of player skill and whether and when you should do that is a whole thread itself.