The stigma plays a role, but a marketing campaign to change that could be more cost effective than the additional cost of light rail. Most BRTs operate exactly like Light Rail with limited crossings, signal control and their own rights of way. In fact many look very similar to Light Rail. The issue with BRT is it doesn’t have the capacity that Light Rail has, which results in similar operational costs, with BRT potentially more expensive.
Brisbane Australia and Ottawa Canada probably have the most robust BRT systems (at least they did when I studied them back in 2003). I know Pittsburgh has BRT, Seattle has some and I think Los Angeles.
C-USA partner city, El Paso, has a very new BRT system and TOD efforts have been made to show BRT can induce development demand like Light Rail. http://sunmetrobrio.net/
For comparison, The Blue Line extension in Charlotte cost $1.1 billion for 9.3 miles (approx $120M per mile). The El Paso BRT cost $27.1 million for 8.6 miles (approx $3 million per mile). Please correct me if I am wrong on the Charlotte numbers.