On the contrary, we have no choice but to use our intutions, at whatever level of training they are at, all the time. So it matters a lot. If A is easier than B iff we learn to think differently, but learning to think differently is harder than just doing B, then A isn't actually easier than B.
Becoming seriously proficient at anything seriously alters the way you think about it, no matter the field. For instance, I play the Cello. Lately, I noticed I only made progress when I understood something, or changed a habit, or let go of some subtle, but ultimately far reaching assumption.
I played the Witness. There's a time based challenge at some point, that I could only beat when I changed the way I thought about those puzzle just so I could go through them faster.
I learned to touch type. To do that, I stopped thinking visually, and instead think kinaesthetically. Then I developed some kind of intuition, where I think a word, and the letters just flow through my fingers. I don't really think at the letter level any more. Neither does anyone proficient with a keyboard. (50 WPM and up).
Our untrained intuitions don't really matter. Seriously learning anything trains us out of them. Programming is no different.
On the contrary, we have no choice but to use our intutions, at whatever level of training they are at, all the time. So it matters a lot. If A is easier than B iff we learn to think differently, but learning to think differently is harder than just doing B, then A isn't actually easier than B.