Not quite.
Raiding didn't "boom" in WLK. There was a healthy pug scene but raid participation on any difficulty was still a minority. You can find Blizzard quotes about that, you can find armory data to show that, etc. 10m also didn't feel nearly as rewarding as it should have, and that is why they made the cata changes. Keep in mind that Normal difficulty then was harder than normal difficulty now. What is currently "normal" is a difficulty they added in MoP that was harder than LFR but much more forgiving than the old Normal.
Raid participation didn't nosedive in Cata. Raid participation was pretty stagnant since the start. LFR wasn't a response to raiding "dying" - It was a response to after several years Blizzard couldn't justify the resources spent on raiding when so few people actually saw the raids. Especially the end raids. Even with catch up mechanics, even with re-releasing Naxx, even with easy no trash filler tiers like ToC, they couldn't get participation up. That's why LFR exists, and since LFR was implemented the amount of raid participation skyrocketed and we get better raids than ever now because Blizzard can justify the resources.
The crying about LFR that we've seen since it was introduced would be hilarious if it wasn't so sad. LFR is the only reason we have quality raids with no boring ass filler tiers like ToC and Firelands where Blizzard just phones it in and recycles all the assets from elsewhere. LFR cost us raiders nothing, hurt us in no way, and gave us fantastic raid tiers for years now. Even icecrown and ulduar are total shitholes compared to each raid tier from the start of MoP onward. Well assuming one can lose their rose tinted goggles for a moment.
Btw weekly raid quests did nothing for raid participation and a BETTER version of weekly raid quests were added in Legion through the follower missions.
You're NEVER going to get people that do LFR as their end game (and there are a lot of them.) to do any kind of organized raiding, and especially not pug raiding where requirements are higher. Blizzard tried to get those casuals into raiding from launch all the way up to Firelands and failed miserably.