Anchoring ends?

I know knots are frowned upon in the knitting world, but I feel as though simply weaving in a tail is not sufficient sometimes, especially at the top of my top down sock. How should I anchor something like that, which will be washed and worn frequently?

I always weave in my ends and I’ve never had the tail come loose even on my socks which have been washed and dried many, many times.

I weave in like this:

I don’t knot either. Weave the tails in for a couple of inches and it is pretty much staying there, especially socks which are usually wool. With wool the ends kind of felt in.