I don’t know about mohair etc., I have never used them (ridden a horse with one) though I have had a look at a few and played around with them. I did use hemp rope till I could get a horse hair mecate (back when I first started doing the hackamore stuff it was a nightmare trying to get the equipment in Australia, there was no ebay or internet stores to go to). Essentially the mecate has to have a few qualities to make it usable.
A) The most important one, and the one I think most people miss is that it has to balance the bosal well since it's changes in the way the bosal moves on the horse's nose that are the commands. So for example, after getting the horse softened up and weaning them off direct pressure commands to signal commands, you want the bosal light, flexible and fairly lose so that it has some movement between you sending the signal and there being any pull, its in-between the signal and direct pull the horse will work (so the opposite almost to what you want at first; at first you want there to be little movement before the pull because you will need to use direct pressure in almost all cases at first and it will skin up the horse if you are not careful). This way the horse learns to move with the weight of the mecate/bosal moving on its nose. This is really crucial stuff, because its the way you get them soft and its the way a thing like a spade bit works in their mouth; signal and balance of the bosal or bit, not direct pressure (and why spade bits are not “leverage bits”). With a bosal there’s no huge problem if you have to give them the occasional pull the get them working something properly (provided its not too hard), once you get to the bit there should be no such thing as a pull directly on that horse's mouth, if you pull direct pressure on the bit, you need to go back to more hackamore generally speaking.
B) This is the thing most people think horse hair mecates are about: The prickliness of the horse hair mecates is about teaching a horse neck reining, which really comes a fair way into their training relatively speaking, you may not actually start the neck reining till the bridling process, I like to get it long before, in a hackamore, personally though (but all the same, you have to go through the process of teaching them to be light and supple through all the other stuff before you get to the neck rein, so think of neck reining as an intermediate to kinda advanced level stuff). Rule of thumb is, mane hair is softer and should be your starting point as you want the horse to move off the slightest amount of stimuli, if the horse doesn’t move off the mane hair that's where tail hair mecates come in; they are harder and pricklier. In conjunction with tail hair you might use a quirt or riding crop to act as kind of like the way you might use spurs, to re-enforce gentler signals through the mecate.
(side note: you will also see horse hair bosals occasionally. They are pretty rare, I have only ever seen 2 on ebay, the first one, which I regret not buying, was really good looking quality, the second one was crap and I wouldn’t waste my money. What they are about is not to “look good in the show ring” as their advertising suggested. They are for a horse that gets heavy in the rawhide bosal, you might use a horse hair bosal for a couple of days to soften them up on the rawhide. So two things here, 1) don’t harden them on a rawhide bosal in the first place and you shouldn’t need the horse hair one; 2) use a horse hair one too much, maybe 3 days or more, and you will harden the horse and may as well start over in a snaffle bit.
C) Horse hair mecates have a little bit of stiffness about them that things like mohair tend not to have and for me that stiffness, and its not much bit just enough, seems to help me feel around with the bosal before I get to a pull on the reins, and it also seems to make the signal clearer and more decisive in a way that I'm not sure something like mohair will, and this stiffness also seems to make them a lot quieter when you are not asking the horse to do anything and are just riding along, they don’t tend to swing about a huge amount (but remember, I have never used mohair so I could be completely wrong). I also read somewhere, could have been in one of the Connell books, can't remember, that horse hair has a fairly low breaking strain to the extent that if you came off and got hung up in it it will snap rather than drag you around behind the horse. I'm not entirely sure about this, could be true or maybe not, don't know (never been willing to test the theory), mine all seem pretty strong, but then I have never really put a lot of weight on them, and indeed the point is that you shouldn’t have to.
So in the end. My preference is for horse hair, but then I'm a bit of a traditionalist and back when I was riding a lot I was a ringer (working cowboy) (ringer and jackaroo are two different things, call a ringer a jackaroo it is an insult actually), and so my hands were pretty hard and the prickliness of them never bothered me, these days though I ride an office chair and a computer all day so it takes a little getting used to. But if you prefer mohair etc. well I guess give it a try. I suppose the best way to think about it would be, by hackamore training a horse I am achieving A result because it all works along B principals. If you can get result A with B principals using a mohair mecate, I guess its fine. But if it upsets the balance of the system then you might be introducing a deficiency that will lead to trouble later. That's just my opinion on it all, doesn’t mean its right.