I've seen too many leather bridles/reins break in a would-be emergency to use webbing. If you really want to use a webbing bridle, I would suggest using leather reins with it, although may look odd.
I used a black Libby's Tack one for ages for everything, including competing as I'm vegan & try to avoid leather as far as poss (which isn't very far with horses).
The big disadvantage is that the headpiece, throat lash & noseband are all separate, so you effectively have 3 narrow straps on top of each other over the poll.
Cat (in avatar) was always busy in his head & in the end I swapped him to a leather Comfort bridle & he was soooo much better immediately so I think the webbing bridle was giving him a headache, esp cos I used to jump him in a dutch gag which creates a lot of poll pressure.
I did ask Libby's if they made a webbing Comfort style bridle or whether they were going to do one, but they said no. Which is a bit rubbish.
My webbing bridle was used every day for a good couple of years & never frayed, & I used to wash it quite a lot in a pillow case. I'm pretty sure it shrunk the first time I washed it.
Where do yours fray? I am very surprised to hear that.
Much prefer leather, but many like the convenience of just bunging them in the washing machine, and all the bright colours you can get
Used to use for endurance but prefered biothane. This is a type of plastic so won't fray in any way and is incredibly easy to care for.
HOWEVER, you must use reins with clips onto the bit and preferably a buckle in the middle as well as biothane will not break in any circumstances. In fact, this would probably go for webbing as well. For this reason if you have a horse which might be silly at gates etc or do alot of jumping, I would stick to leather.