"Just the first raid of each expansion" sounds like a terrible requirement, and would likely skew the roulettes even more in favour of maybe coming up quicker but rarely being anything but that first duty, because it only takes one person to drag it down there.
I've said before, I think they handled the "incentivise HW/SB alliance raids" step of the Bozja relics really poorly.
The pacing is dreadful. You have to do it all in a rush, six of each raid series, before you can progress to the next step of the relic – and then you never touch it again for subsequent relics.
It also gave equal weight to all three raids in the series, giving people no incentive to unlock beyond the first and easiest raid of the set. Result: endless Void Ark and Rabanastre. (Likewise for the eight-man raids, where the frequency of duties suggests that a lot of people never unlocked beyond #3 of 12 – probably not coincidentally, the first of the series that will give you the second type of tokens.)
It could have been handled so much better.
ARR had already shown a better way, with unique tokens dropping from each of the three alliance raids for Gift of the Archmagus. This could have been done for the Bozja relics: require collecting a set of three tokens from the three raids, one complete set required per relic. People then do less runs at once, more slowly over time, and have to unlock and run all three raids equally.
Likewise for the eight-man raids. Drop unique tokens from the final raid of each tier, and force people to unlock all twelve raids to get the tokens. No alternate sources, just straight up "if you want your relic, you need to have unlocked all optional content in the game".
In short, create a grind that encourages a width of content being unlocked, and benefits those who put in the work earlier. Not just incentivising a single duty that can be run over and over while neglecting the rest.