Should I replace bathroom OSB subfloor with plywood?
OSB was an idea introduced in the late 1970s and caught fire in the 1980s.  After a few decades of use, compared to plywood, OSB just does not hold up as well. You would have thought wood manufacturers would have learned from manufacturers of plastics, and moved toward fiber-mat combination for strength and durability... guess not. 

I have observed plywood homes which have solid (but squeaky) sub floors which are several decades old and still in excellent shape.  On the other hand I have observed sub floors which are OSB and just a few years old and crumbling into their original configuration (saw dust).  

Environmentalist may very well like OSB but for wet applications, its not desirable.  In wet applications mold, mildew and rot are the constant battle. Bathrooms in homes are just not configured to deal with these issues, Bathrooms in residential construction don't disperse water/humidity from the air, and usually have very little air movement, most being tied to only one register outlet of the central air system.  It helps if one keeps their central air system fan in constant "on" mode as opposed to allowing it to cycle off.