No. We haven’t proven that minhag overrides halacha. We’ve proven that sometimes when we say minhag, we mean how you and your group hold in the halachah. Eg. Those of us who wrap teffilin on chol hamoed (especially those who do so with a brachah) hold that it is required. Those who don’t hold that you can’t. We don’t look at the other side as thought they’re breaking halachah through their minhag, we just respectfully disagree on what the halacha is. That’s really what minhag is, respectful disagreements in the halachah. This includes not eating in the Sukkah on Sh”A
We don’t wear techeiles for the same reason we don’t bring korbanos to the beis hamikdash: it’s impossible!