A Combined martingale is a Standing and running combined into one piece - haven't seen one for years and I've never had to make one.
The Irish martingale is primarily used in racing - it's basically a short strap ( about 6" ) with a ring on each end that the reins go through, this helps to keep the reins from parting or flapping around too much which would be dangerous considering the activity, ever seen a horse go over The Chair at Aintree and you get the picture
A bib martingale is like a running martingale with a panel of leather joining the two ring straps together - so it's like a combined running martingale and Irish martingale , in the past primarily used for racing ( I've made about 50 for Newmarket ) but now I also see them in the showjumping circuit
The triangular panel is needed or there would be a gap which a horse could put it's leg through , which would be a disaster.
A Market Harborough is like a running martingale - except that the two ring straps are a lot longer and have a small clip on each end - these pass through the bit and onto a small 'd' fitted onto a pair of reins, they have a similar effect as a running martingale but are a lot stronger . They also have a similar effect to draw reins in bringing the head down but the downwards pressure is released when the horses head is in the correct position ( draw reins do not )
Although I would agree with you in that most of these are not needed in normal circumstances they are very useful as training aids and should be removed when not needed, some are however almost essential in competitions such as showjumping / cross country or racing , as the horse gets a lot of adrenaline in its system ( and most competition horses are either warmblood or hotblood ) and get rather out of hand and excitable.
I wouldn't call John Whittaker / Rodrigo Pessoa / Zara Phillips etc novice riders , they do use martingales for good reason - and I don't think they need to work on their riding .
I hope that clears up the martingale issue -