I did undergrad degrees in both CogSci and CompSci. Both have been virtually irrelevant to me in my software development career so far. Both were valuable to me for reasons of self-actualization. I would advise you to do what you find personally valuable.
I would not say that CompSci "stifles creativity", nor even that it ignores web development entirely (although that's a murkier point, and mobile is too new for most universities to teach it, which is just how it goes). But I would say that the overlap between what universities know how to teach, and what is relevant to working software development (in emerging areas and in well-travelled areas) is very small indeed, perhaps a few percent of each.
When advising my lead on a hire/no-hire decision, I would give absolutely no weight to the degree or lack thereof, and would give weight to a combination of 1) real experience, and 2) my (flawed and subjective) judgement of intelligence and skills.
All that said, apparently some companies still value the piece of paper. I think there are three levels of degree-ness from those companies' perspective: correct degree (cmpt, eng, maybe math), other degree(english lit, archeology), no degree. And I think that those companies will see a CogSci degree as virtually equivalent to a History degree: "Oh, I guess he's got a degree, so that's nice, but the content of the degree is not what we might hire him for".
Does anyone take academic HCI seriously in industry?