the cost of buying the stuff is dirt cheap, but that could be the reason it is cheap and not worth using.
Or most here have access to these willow trees and it must the tree to make it from.
There are several reasons why people here make charcoal, it really depends on the type of BP you are after. If it is just for rockets or to use in fountains as a filler to add effects to then you can use most types of charcoal as it does not need to be that powerful. As a general rule you should look at the density of the wood, and if the wood weighs a lot for a small volume it will find more uses in fountains and rockets, if it doesn't weigh a lot then it can be used for making much more powerful BP.
As an example, think of the difference in weight between pine and balsa, if you made 2 lots of BP, one with each, and made an equal sized trail of them then the lighter balsa charcoal one would have burnt to the end before the pine one was even half way.
Also when making your own charcoal you can vary the amount of volatiles still left in the wood. By only just turning it to charcoal you can make slightly more sensitive BP because a lot of the flammable oils and things are still left in the wood. If you 'cook' it for a bit longer then you will end up with slower BP. Making your own charcoal gives a lot greater control over the burn rate, as you know exactly whats happened to the wood.
I do not know a lot about mesquite and sage trees, but cut off a reasonable sized piece, and compare the weight of it with a similar sized piece of willow, or other light wood. If it feels really heavy in comparison then you know it will make slow burning BP.
For rockets I just use general hardwood charcoal, then something more powerful for the break on the header such as balsa or willow BP.
Here is a list of the sorts you can use
Dense (slow burn rate)
Pine
Spruce
Oak
Light (fast burn rate)
Willow
Alder
Balsa
Hemp
Rye (this is said to be much more sensitive)
Try not to get confused between hardwoods and softwoods etc. and density, because balsa is classified as a hardwood yet it is the lightest wood that I know of!
Hope this helps.
You can never have a long enough fuse...