Before anything let's pay attention to the building and fire code requirements and also if there is any local restrictions in place.
Building code requires that wood used as an interior finish material meet flame-spread requirements.
Wood joists, 16 inches on center rating is 10 minutes and for 1/2" sheetrock is 15 minutes. according to Component Additive Method (CAM) for Calculating and Demonstrating Assembly Fire Endurance, Design for Code Acceptance 4, American Wood Council, www.awc.org. So you have 25 min with sheetrock before floor failure and you have 10 min without sheetrock under normal fire spread.
Other than that even if you can leave that exposed, only very few who can find inspiration in it. I can see this being a barn style home, or a loft with 12'-16' ceilings, or a cabin in the middle of nowhere or something commercial yes, but me personally looking at something like this every day, I just don't see any attraction in it.
With that being said, that ceiling will always be a dust attraction, and if you have second floor, each time someone walks up, etc not only it will be noisy, you will have dust particles being released from wood and flow around all over the place... IMO to have something exposed in a living area creates unhealthy environment.
Good luck.
Q
one of few fans with 100 CRI.
Q