Bad-luck protection isn't working because I've been doing Mythic+ dungeons all day and no Legendary drop for me! Please fix Blizzard!
Seriously though, it's not bad-luck protection, it's EXTREME bad-luck protection. It doesn't mean that you will get a Legendary to drop in 1-2 weeks, even if you spend most of your WoW time doing M+ dungeons and clearing the raid on LFR/NM/HC (and M for those with guilds).
I got my first one yesterday, which was ~2 days after I unlocked my Equip 2x Legendary perk. I've been playing the same character/spec since Legion's release on the EU and I've cleared the raid and done multiple Mythic+ dungeons since they were released. That is around 6-7 weeks of completing PvE content that has a chance to give me a Legendary.
Now what the devs should really look at is balancing Legendaries. The one I got was semi-decent, but luckily it was still an upgrade for my class. However, there are some very unfortunate players out there that obtained a Legendary (CC ring comes to mind) which isn't even an upgrade for them, as a result their bad-luck protection reset back to its default value, now THAT is bad-luck. Hopefully we will see some Legendary balance fixes as there's a huge gap between some Legendaries.