"It seems to me that the CFM56 is a more popular sale because
they are so much quieter and more efficient than JT8-D's. If you see a
KC-135R or a re-engined DC-8 which both have CFM56's you will see exactly what I mean."
PW never bid on the KC-135 contract, nor did they bid on the Super 71 conversion. CFM won by default. PW had a difficult enough time building the JT8D-200 for the influx of MD-80 orders, they had no ability nor the foresight to see this market.
In fact the PW JT3D to JT8D re-engining program didn't officially begin until 1996. So there was no competition between CFM and PW, CFM won as the only bidder. PW hasn't really offered this program to many customers yet, however it is in the running for a USAF contract to re-engine JSTARS aircraft due to ground clearance problems w/ the CFM. Additionally, it is still possible that PW with the JT8D, could win another contract to re-engine some AF reserve and Air National Guard aircraft. All of these proposals combined with the other airlines and governments that could use new engines make it very likely that PW will at least have some customers.
" JT8-D's are quite loud with a really high pitch idle
and this can be a turn off to customers who are looking to re-engine
older jets. "
The JT8D-200 is Stage III compliant without a hushkit, as is the CFM-56. I think you are confusing the classic, straight-8 engines with the newer -200s, which are much, much quieter.
Though the some CFM56 models are quieter than the JT8D, and all are more efficent, it doesn't matter because PW until 1996 chose to stay out of this market. PW's advantage here is price, PW is able to price JT8D-200's at a much lower purchase price than CFM's. For many of the struggling airlines and governments that are looking to re-engine, purchase price is the most important. Though your facts are correct, your speaking points about why the CFM is more popular cannot be applied.