I want to point out that "Pure Healer" could mean more than just high potency healing and no utility. In the job actions trailer, two abilities shown had a water theme to them and were cast on the White Mage casting them. In every other circumstance where a healing ability or buff was showcased, it was used on the standby ally such as the Scholar's first action that threw a page of the grimoire at their ally, the tether, or even the Astrologian's cards.

These two water animations weren't used on the ally, so they are likely self-buffs that do something, we just don't know what yet. There are many possibilities for these to apply some form of utility that contributes to the "Pure Healer" concept.

Also note that of all the new UI features, the White Mage's lilies don't have any kind of timer. Presumably, they can be kept up indefinitely until an action that requires expending the lilies is used. If our information about each lily providing a chance to shorten cast times is accurate, it isn't unreasonable to think that having all three grants a 100% chance to marginally shorten cast times (say 5% maybe). If this is indefinite, that can really up their HPS and DPS over the course of a fight, meaning they could end up bringing more raid DPS than the other healers in the hands of a skilled player.