I buy Nike running shoes because they are cheap, durable and comfortable, I don't actually use the to run.
The other obvious answer to this question is "because they are status symbols", for some people anyway.
Shoes, sure, because they do make great running shoes, and I suppose - forgive me - if one doesn't care about making a good visual impression, they are quite comfortable for everyday wear. I'm more confused by the visors and shirts and such. Any ostensible status garnered by being an ad is immediately overbalanced by the questionable taste and decisions of its wearer.
You seem to be going to great lengths to avoid confronting the fact that most people simply don't care about logos, or, if they do, are doing it to fit in with whatever crowd they're a part of.
I think the OP was more focused on basic clothing items and accessories like tee shirts with logos.
I would give their running shoes a pass as my downshifters are amazing - they make me want to run - so quite comfortable and functional. A Nike branded shirt or pants however are just decorated cloth.