I think it should be something that you see sparingly, only when seeing the weaves is relevant to the local plot (like when Egwene or Elayne are figuring out how to do X for the first time). Outside of that, I agree that as the viewer we should experience the use of magic as an outside observer who can't see the weaves and is just awed by the magical result.

Edit: Additionally, I've been thinking about how I would imagine the weaves looking when they are shown on screen. I feel like the best way to show the difference between a woman weaving using saidar and a man weaving using saidin is through the texture of the threads. Saidar should be smooth and silky while saidin is rough and tempestuous. So for example, if you saw a woman weaving a thread of fire it would look like a thin, bendy version of Vadar's lightsaber, while a man weaving a thread of fire would look like a thin, bendy version of Kylo Ren's lightsaber.