Where less is more
I read that the factories have analyzed knot performance with micro-photography, as well as carefully controlled and measured comparison tests. An important discovery was that knots that fail prematurely usually slip internally before they come apart; hence the pigtail curls. Knot choice is important, and there are several that produce tippet-to-hook connections of above 90%. I like the double-loop cinch and the Pitzen (Pitzer?) knots.
But the problem with tying any knot is a matter of technique: you've got to get ALL the slack out of your knot in order to achieve optimum strength. After tying on a fly, have you ever pulled on the tag end with your teeth or pliers? The tag end got longer, didn't it? I don't think that's stretching; rather, it's the result of pulling slack out of the knot. And that makes it as strong as it can be. You can pull on it until it breaks (at that knot's maximum strength), but it won't slip.
About wraps: Most knots are devices designed to create friction, so much friction that the knot can't pull loose. The more wraps, the more friction. But there's a point of diminishing returns, when too many wraps creates so much friction that the knot can't be pulled tight. Try, as an experiment, tying a cinch-style knot with 10-12 wraps. You can't pull it tight, right? Tie it again with fewer wraps until you find the optimum number that allows you to pull it tight. Heavy tippet, and tippet tied with stiff mono, and some fleurocarbon, requires fewer wraps for an optimum cinch knot than 7X tippet.