When making an instrument, all aspects should be considered together, as well as separately. Thus, material of the didgeridoo is in relation to its design and your goals. Generally, hard wood provides more high frequencies because hard materials do not absorb short waved sounds, i.e. high pitched sounds. Dense hard woods also provide more power since again they reflect sound rather than absorb it.
Let’s take an example of one didgeridoo design. Let’s make things very simple and presume you want a didgeridoo with a lot of bass and acoustic power. So, if you make a wide cylindrical instrument, you have the bass, but not the power. For that, you must make a bell, prolong the instrument and tighten it a (little) bit. Now you have the power and the bass, but it can tend to be muddy. You can solve at least a part of this problem by using very hard wood, which will reflect more mids and highs and therefore compensate part of the spectrum.
In real life, if you listen closely, these phenomena are much deeper and more subtle, and human ear can recognize many colours of sounds. What it sums up to is that we like the aesthetics of (very) hard wood sound, and we also use their fantastic ability to make and reflect sound to reach the fullest spectrum possible.