a classroom full of PhDs may be architecturally similar to an open-floor plan startup office, but the quality of sitting in one and thinking is different - mainly, it's quieter in a classroom. Quieter is good for thinking.
The startups I've seen don't particularly use whiteboards.
As far as working from home goes, it seems you each agree that being comfortable with ones workspace and environment impacts productivity. That said, one is more likely to have a comfortable and productive work environment when it is up to him/her to decide what equipment to use and where, which a home office lends itself to more than an office, especially on a corporate cube-farm level. Sure, some individuals may not be as productive at a comfortable workspace in the home, but that is the individual. Working from home is not for everyone, but those who find they are more focused and productive in the home environment ought to have that choice.