The three healers are not created equally in stats and have different base CHR, PIE, DHR, DET, HP/MP, etc. This plays the biggest influence in regards to the weapons each healer uses, as they tend to provide different stat bonuses along with meld restrictions. Keep in mind that you can increase CHR and DHR to the nines, but it is still RNG for them to actually trigger. Stats like PIE, VIT, DET build on the base and are not reliant on RNG.

The issue with the latter melds though is that they will not add much if anything to your overall DPS. However, MP is your lifeblood, and you also need to stay alive. Other than one-shots, healers are often done in when their HP is too low to survive unavoidable damage, and this happens a lot when they are learning a fight. They are also crippled if the fight goes on longer than their resources will allow. Again, this is something that happens due to inexperience not only from them, but possibly their teammates as well.

So those PIE/VIT/DET builds are VERY helpful when learning a fight. After you are comfortable and can do it standing on your head, go all out CHR/DHR where they are allowed. Take advantage of materia removal if you have the means to easily reacquire lost materia, which you should if you care about optimization.

Spell speed is a stat that becomes more negligible the more proactive the healer is, and raid damage is very predictable. This is another training wheel stat for when you are learning a fight because the overall benefit from CHR/DHR builds will be greater in terms of your overall DPS and clear times so long as you can actually optimize your abilities. If you cannot, then you might be better off with builds that are not reliant on a RNG since in order to reduce the RNG factor, you MUST optimize.