Are there enough variation of spells to make it fun for a dedicated healer (CON)

[Wyngale]

What are the current state of FFXIV ?
Are there enough variation of spells to make it fun for a dedicated healer?

Unfortunately no. You use 1 or 2 spells for healing (usually alternating between Cure and Sacrifice). Due to AOE you can usually hit all the injured people together. The status effect situation is a mess. Except for paralyze, curing status effects is pointless, and the most serious status effects (like petrify) don't have cures.

Or are healing spells on long enough cooldown to make a "healer and" work better than a pure healer?

Heals have the shortest cast time and cooldown of all spells, you can almost spam them continuously once you have Fastcast. This means that healing can always be done on-demand freeing you to do other things if everyone is topped off.

Or have the solved it in a nother way (ex by making Crowdcontrol better in some situation and so favour "healer and").

They have solved it by making every mage an on-demand healer. Because healing is so easy due to AOE and short cast times they can get away with this.