I've used this method to tie all my shoes for more than a decade and it holds much better than the granny knot, which I'd guess is probably 50% of people (as whether not you end up with a granny or a bow knot is just the toss of a coin). The benefit of Ian's tying method is that it is impossible to end up with a granny knot.
My shoes never* come untied, without needing to resort to a "double-knot".
* Except my Sperry Docksiders, which have leather laces and don't seem to keep any kind of knot very well.
Maybe I did the Ian knot wrong. Don't have a problem with the knot I use so not investigating further.
I will say that I cinch the knot tighter with leather laces than any other material because, like you mentioned, they are fussy.
I don't know why anybody makes round laces, especially out of a material that slips.
I have a pair of dress shoes that came with round laces. Even with a "correct" knot, even with double-knotting, they always came undone. I replaced the laces with standard flat laces. They might not look as good, but they look better than having to re-tie them every 30 minutes.