For most people, yes, any bike will do, there won't be any special affection for one over another; it'll be a "tool of choice".

For others, like me, there are special needs/circumstances that require a bit more refinement in choice.

Being 6'1" isn't extraordinary, but I have long arms & legs, and this means I have to look art the bigger range of frame sizes -- not even an option for a big-box-store bike. I have back issues that preclude using rigid or hardtail bikes. Full suspension is necessary. Not having tried the Cane Creek Thudbuster suspension post, that'd be about the ONLY alternative I'd have left (and at $150+ for the thing, not a casual tryout); suspension posts in hardtails has not been something I can do long-term.

I also ride hard and get a little silly; I've cracked 3 MTB frames in a decade, not even doing extreme stuff -- it's just a combination of my size, my riding habits, and a hit-or-miss experience in quality.

So for ME, no -- not just any bike will do as a commuter.