Brookwood Parkway is a ways from where I live, so I actually haven't ridden it since the area became developed...that's a long while. Got to get over there one of these days to see.
It's probably posted 55mph, because the road is still probably regarded as rural by the county road engineers, state dept of transpo, etc. Not even having seen it, I'm inclined to agree it probably needs good bike lanes in addition to the MUP. There are excellent examples of fast roads with good bike lanes, such as Hwy 47 between Forest Grove and Gaston.
A basic reason Brookwood doesn't have nice wide bike lanes probably has to do with some old road easement that planners are trying to cram a much higher motor vehicle carrying capacity onto. People are slow to spend more money to widen the easement to allow for an increase in volume of motor vehicles carried and to provide for good bike lanes as well. For a long time already, it's been time to slow down on widening roads so they can carry a greater number of motor vehicles; unfortunately, this doesn't seem to be a very popularly received view of how to use roadways.