I'd suspect the results would be different, the fact a commute is forced puts your brain into the mode where you solve creative problems in the background without thinking about them. There are good reasons ideas come out of nowhere to you in the shower or on a bus.
That said I'd never ever have a 1+ hour commutes, 30 minutes is plenty but I have noticed a difference in inspiration this year and I put it down to this.
Once you throw mass transit into the mix, a long commute also becomes dedicated reading/napping/web-surfing/project-management/side-project time.
I was doing 90 minutes each way, four days a week, before; I'm currently not worried about going back to three days a week, although I'm a little curious if I'll feel differently once it happens.
"a commute is forced puts your brain into the mode where you solve creative problems in the background without thinking about them"
I don't think about work outside of work, which includes commuting. I may have an epiphany while showering or talking a walk, but in the car I listen to music or podcasts. That is Me Time, not Employer Time.
"You might not be thinking about work, but your brain is."
This is definitely true after work sometimes, but a commute is not necessary for this. Walking helps similarly and is healthier, too. For me personally, I tune everything out and listen to music most of the time while commuting, or simply meditate (specifically not dwelling on any thoughts).
"Maybe I care about this more because I'm a designer so, creativity is what I'm judged on."
I'm not sure if you intended this, but this could be read that you're implying that programming is not a creative profession. Which is wholly false.
Part of tackling hard problems is coming up with creative solutions. One absolutely needs creativity and vision to architect larger applications and coordinated services.
I've met accountants that are more creative than some jazz musicians, but the creative work they do is much more abstract and not as intrinsically understandable as a musician that's improvising on a tune.
That said I'd never ever have a 1+ hour commutes, 30 minutes is plenty but I have noticed a difference in inspiration this year and I put it down to this.