Variant and Criterion were missed opportunities, for a lot of different reasons (rewards, failing to address midcore difficulty, etc), I know, but that's not what I actually disliked the most in that specific content.
In fact, I did like that it was something new and fresh, and that SE went all the way to answer to the demand of getting harder light party content is commendable, I want to get this out of the way. The more they try new things, the less stale the game, even if it fails to meet expectations. I also did like that variants could be done solo so that I can just chill and enjoy it at my own pace (but more on this later). Even for Criterion, it was a change of pace and it was kind of chill to prog and I did like this.
However my big gripe with variants and criterion is something I also despised this with Delubrum, which is ironically often considered a great piece of content (I did like the Delubrum encounters though): the further demolition of the role trinity and identity.
In fact, if you take Variant, it's designed for it to be role agnostic, which fundamentally rubs me the wrong way already because it removes most of the role and identity of healers, tanks etc. Everybody essentially becomes a glorified DPS, and anybody can take defensive mitigation or healing as a duty action. It completely reduces whatever is left of specific roles and duties to fill when you queue up as any job, and makes everybody an interchangeable piece on the board, where everybody can raise, heal or tank. This is literally what pushed me away from playing Variant in any group, and I thank providence that they provided a solo option with the duty actions, which is the only place where they made any sense. Before anybody says that it's like deep dungeons, I'd retort that no, it's not. Role agnosticism in deep dungeons make a lot more sense because deep dungeons aren't about the standard battle content.
And then, if you take criterion, unless it's the savage edition, everybody can raise, and since the fights are essentially designed a bit ala delubrum, it's 110% focused on mechanical execution rather than true party damage, busters and whatnot. Those fights have never felt closer to me than to arbitrary job colours where you only get support and dps roles because partner and spread mechanics are everywhere and require something to base themselves on. Even if more squishy than a tank, I can perfectly tank the bosses for extended amounts of time as a dps or a healer. Now, I understand why they gave raises to everybody, because unlike for 8 man parties, if the healer dies, it's checkmate (unless you have a SMN/RDM). I don't have an alternative answer for this to be honest (maybe a self re-raise duty action on the healer?), but matter of the fact is, it still compounds furthermore the slow deletion of roles and job based mechanics and toolkits that's been plaguing the game for a while.
Last but not least, criterion doubles down on mechanics and tries to be super fancy with overcomplicated mechanics like that pinboard or those samurai shadow clones and whatnot to make up for the lack of body checks. If anything it compounds the issue even further by showing how much of an empty shell everything else is those days, because that's the only thing remaining in the game that can bring any amount of challenge.