Q:

What are the technical reasons that there are no frequency modulated transmissions on the long- and medium wave?

Why are there no frequency modulated broadcasts on the long/medium/short wave, but only on VHF? I'm sure there are many historical and political reasons (long/medium/short wave were already in use for AM when FM radio was developed, VHF still had lots of free bandwidth), but are there also technical reasons? 
FM radio gives a better sound quality than AM. Common FM on VHF also uses a much broader bandwidth and interchannel spacing than MW AM, so using the same bandwidth per channel much fewer FM channels would fit in the MW band than AM channels. But narrowband FM can be used with similar interchannel spacing as is typical for AM, so this is no reason not to use frequency modulation.
So are there any technical reasons why narrowband FM broadcasting is not used on long/medium/short wave, and if so what are they? I'm assuming that even narrowband FM would give better audio quality than AM, am I wrong about that?
(disclaimer: maybe there have been some FM transmissions on MW that I'm not aware of, in that case please read this question as "why are there nearly no FM broadcasts on the L/M/SW ...")
(I'm asking out of historical interest. I'm not planning on setting up any FM on MW or something)

A:

So, the bandwidth argument is the dominant one. You need to incorporate the full Carson Bandwidth in your channel spacing, not only the frequency deviation! As explained in my answer to your previous question, that must be significantly larger than the bandwidth of the same audio signal in AM.
Aside from that, as always in Ham usage: historical reasons.
If you'd ask me, no sense in doing FM, either. There's digital voice modes that have a far superior spectral efficiency (that's a measure for how much  info you can get across per second per bandwidth).
I'd recommend looking at DRM (Digital Radio Mondiale), a broadly adapted narrowband broadcast mode than can give you very clear voice over noisy 3 kHz channels. That's what India and Brazil are doing to replace their AM MW broadcast stations. Not "small scale bleeding edge". This is literally "state of the art for billions of people" tech; using FM to make more of the MW spectrum is half a step back, not a step forward.
If you need really narrow band communications (and that's what you'd want if you're working MW with a lot of people), then the digital voice modes of FreeDV are what I'd look into. 1.25 kHz channels with good voice communication, in any situation superior to AM, and not comparable to FM at all, because FM wouldn't even remotely allow voice communication at 1.25 kHz CBW. You don't need fancy hardware to use it.
So, FM was never an option on low frequencies simply due to bandwidth constraints, and digital modes are the logical step from AM.
I can only recommend to head over to the Codec2 site, and listen in – Codec2 is the audio codec used within FreeDV. Listen to the 1300 bps sample and ask yourself whether a 1.25 kHz AM channel would have offered a comparable quality (and before the "digital modes don't degrade gracefully" people show up: at SNRs where this works, you won't be hearing anything but static over AM. Also, FreeDV by default uses FEC, so yeah, it degrades graceful – by not degrading at all at first, and after that, the codec is still pretty robust against bit errors and does indeed degrade rather graceful, compared to AM, especially in the presence of burst interferers). 

