Ok focusing on your previous point, there is a likelihood that relative to the previous tiers, there is potentiality of a feeling of a bigger shortage than before because in the design of 2H, 2T and 4DPS and in relation to week to week (beyond week 1), we can safely assume that more DPS have obtained clears after week 1 compared to the same amount of Healers or Tanks in PF and we know this based off the fact that a heavy majority of the playerbase overall mains DPS roles. That's not anything out of the ordinary.
Something else we can pull though is still that many more tanks and healers entered the tier this time around. Now what we are seeing is a massive shift to PCT. It is the top DPS in terms of parses overall but it is not a specific exclusive reason as to why the clears are far higher than average (more than 3x on average). The core reason of why the tier has been cleared decisively quicker than others is because two specific things aligned, 1) The initial balancing of PCT which was very strong, and the XIV team admitting to not having enough time to adjust PCT AND rebalance classes AND rebalance the raid for DPS checks, so they basically brought the other jobs up to align with PCT without tuning the raid to the increased DPS.
We knew this, they said this. So by that, perhaps we can blame the initial overall issue on PCT but it's not like the job itself is driving these numbers to this degree. It's just the raid itself isn't accounting for the high DPS of all jobs.
But the second reason is actually the mechanics themselves. There is a surprising lack of hard body checks this tier. There are some positioning checks here and there but PF struggles the most with body checks, basically mechanics that if a certain amount of people aren't at point A when thing goes off, mechanic auto deletes everyone. All included DoTs for failed mechs this tier are easily GCD healed through. Something like the Pandemonium fight last tier did NOT allow this, which not only combined aggressive body checks with very short timing on mechanic overlap but overall way more 1 shots of groups of 3+ players.
Savage imo, hasn't ever had a protection from shortages. It's just that a lot more people entered the raid tier, and more of that new group are playing DPS over Healers and tanks. This has been the same issue every single tier though. There has never been a tier where by Week 6, Healers and Tanks were abound after reset day.
Most people in PF leave the raid scene after getting their bis.
As for Healer role having even lower numbers than tanks, it is the MOST unpopular role as always, especially in PF because it has the most responsibility compared to Tanks or DPS. It not only has to plan on it's mitigation but also sufficiently heal damage (both expected and unexpected adjustments), while also managing MP, while also doing DPS, while also doing mechanics/positioning. A healer death is far more costly to the success of a raid fight, even after everyone has gear. In PF, where the average unexpected events is the norm, a decent amount of Healer resources tend to be required to keep a run together. This is why when you see tiers that introduce body checks or aggressive DoT ticks with AoEs (ala tree boss) where GCD healing becomes alot more required, the Healer population tends to shrink and alot leave the scene. When the Healer checks are relatively manageable, the Healer pop goes back up but it's still a shortage. Not to mention, there are ALOT of greedy Healers in PF that would prefer to Glare then use a single GCD heal when it's clear its required to survive or top up for big damage. Thus, there is really no direct solution to the shortage of healers without perhaps changing the dynamic of the games design (and giving everyone more personal responsibility on there health management)
If you want to see more Healers in PF, you have to mitigate the responsibility requirement healers innately deal with. Otherwise, you can never fix any shortage issue on the role overall. You are not gonna convince DPS to Heal in mass and your best offer is more responsibility with everything in spades. That's a bad deal no one is really signing up for. It does not matter if you add more DPS options, or better utilize the Healer kit in raid.
There are options beyond still for SE to utilize like, job in need bonuses, that they can try to reward guaranteed drops for players willing to fill into deficient roles but not much beyond that and I wouldn't expect any MAJOR deterrents to shortages from even that.