So what I'm getting, in a nutshell, is that if you narrow-band, both transmitters and receivers need to have it done...
Absolutely, both TX and RX need to be done, or there WILL be severe performance loss.
and then the best is that it will have as good coverage as wide.
Apparently, and according to participants in this thread, that would depend on who you're talking to. Theoretically, reducing bandwidth (while maintaining equal noise figure), there should be a slight improvement in performance. But there are plenty of people out there declaring substantial loss in coverage. In my personal experience, where both TX and RX were properly narrowbanded, I believe performance is about equal. I have not made measurements to compare.
So if you have the choice, like with GMRS or VHF/UHF Ham, the best option is to stick with wide.
If there is a choice, yes. The advantage with wider bandwidth is a better signal to noise ratio when the receiver is saturated (full quieting). The choice has nothing to do with weak signal performance. This is why FM broadcast uses 75 KHz deviation. Old analog FM microwave radios used something like 200 KHz deviation per multiplexed channel, all for S/N ratio purposes. But FM broadcast and microwave operate on the assumption that received signal levels are well into saturation, with 40 db fade margins or more.
Also, if the transmitter is narrow, but the receiver is wide, audio will still come through, howbeit degraded and with, more than likely, decreased coverage.
Is this correct?
Sort of. The decreased coverage isn't a result of weaker carriers, it's the result of much lower demodulated audio. As signals get to be weak, an FM receiver starts to noise up. If the modulation from the transmitter fills up the receive IF passband properly, the signal can noise up considerably before it becomes unintelligible (threshold).
A narrow transmitter into a wide receiver, however, will still noise up, but at some point, the noise now equals or exceeds the level or the recovered audio, and therefor it's unintelligible, long before the received carrier is too weak to demodulate, hence the perceived reduction in range.