Horizontal progression? In MY theme park?!

[Zojha]

I don't think you understand horizontal progression.

Truth be told, most people don't seem to. Heck, I constantly see people confusing it with special effects.

Ultimately, all progression is progression. It's a one-way street on which you can only progress, stagnate, or regress in a single direction and only the first of those three is deemed motivating. In computer terms, progression typically means two things:
a) A checkmark is cleared (Raid, Story progression)
b) A number goes up (Combat stats, e.g. DPS).

So called "horizontal" progression doesn't get rid of that, because it wouldn't be progression at all otherwise. All it does is to take the generic "combat" progression line and feathers it into multiple sub-purposes that each progress "vertically" individually.
By nature, given equal gear acquisition rates, that's going to mean more grinding, because you no longer have one "best" set, but multiple, one for each purpose, which may or may not overlap. And it also relies on there actually being multiple relevant purposes in the combat system itself to work. Which... is probably the biggest issue when trying to expand it in FFXIV.

Special effects on gear are entirely separate from that and can be either "vertical", i.e. represent an upgrade in performance or "horizontal", i.e. represent a different purpose. "Randomly spawns 3 Voidlings to deal damage" is a different purpose than "Randomly erects a barrier that blocks 15% of your max HP", thus they are "horizontal". They are also "vertical", because it's a clear improvement of combat performance over "nothing at all" or a weaker version of the same effect (like 1 Voidling/5% max HP). Same goes for less fancy stats like +15 Survival Stat vs +15 Damage Stat, it's just less smoke and mirrors there.

Neither of the two has much to do with how long content remains relevant. Barring plain enjoyment, a piece of content is relevant for as long as it represents progression. For gear, that means the rewards need to be better than something you already have. And in the "horizontal" model, being better in general is simply replaced with being better at some (ideally relevant) purpose. Since "horizontal" progression ceteris paribus requires more grinding, it naturally boosts longevity of content as well. How much depends on the degree of difference between the different "best" sets.
However, ultimately longevity is mostly decided by the rate at which gear (or any other progression metric) is acquired. That's obvious: Since the relevancy of the content is tied to the progression it provides, the sooner you get that progression, the sooner it becomes irrelevant.

A good example here is leveling content: If you level multiple jobs, XP remains a relevant reward for longer than if you only level one. Thus, the content remains relevant longer, i.e. has a higher longevity. Since leveling multiple jobs is not mandatory however, this is entirely optional and that's a good thing. But it matters little if you can just boost yourself to max easily. Gear follows the same principle. You can have a million different gear purposes and item slots, if you can get all items for free at a vendor in the starting area, the longevity of that is as long as it takes to navigate the menus.

Personally? I'd loath to try and support more "horizontal" progression within the individual jobs while the overarching job progression is still such a PITA to participate in. Most of the time, you can barely gear up your basic trinity roles before the gear becomes obsolete due to caps and other pacing measures. Adding more progression on the job level would increase that issue exponentially.