The main problems with HF are partly the low bandwidth (follows from the low frequency, unless you are prepared to gobble up the entire HF range for one user), partly that the channel is dominated by fading. Traditionally, the 'solution' to the second problem is to shrug one's shoulders and say "HF is tricky", while reducing the bandwidth another couple orders of magnitude to get through the crappy channel.
Cellular phones also use channels dominated by fading. Enormous effort has been made to achieve truly breathtaking performance on such channels by using tremendously sophisticated modulation and signal processing methods. That effort has been driven and funded by the desire for higher capacity mobile networks, but the results could be applied elsewhere.
By comparison, even state of the art HF technology is primitive. DSP on an SSB signal is a remarkable improvement, but all you are really getting, as far as I know, is steeper IF filters, lower noise figures, sharper notches when needed, etc; it's still just an SSB signal.
Adapting cellular phone technology to the HF channel, such as sophisticated coding and modulation schemes, maybe Rake receivers, perhaps OFDM and so on, could take HF communication to a completely new level.
It would take some effort for sure, since all relevant parameters are orders of magnitude different; not just the frequency (a few MHz vs. a couple GHz), but fading times etc. Also, a lot of the effort in cellular phone technology is aimed at solving the multiple access problem, scheduling and so on, which it is not obvious how it would apply to the HF world. But it sounds like an interesting problem!
(Not having radios as a hobby, I only design them 'cuz someone pays me to...)