Aetherytes, Garleans, and You!

[Enkidoh]

Even long before that reference though, there was already mention in the game about anima still being the factor behind whether someone could teleport or not (and how often) - the gate guard next to the aetheryte in each of the three starting city states will explain about this if you speak to them as early as when you first attuned to it at the start of the game:

"As Return merely involves allowing the body to be drawn back to the strongest aetherial beacon - one's home point - it is fairly easy to execute and requires very little spiritual exertion. Usually a few moments of rest is all that is needed before it is safe to attempt another jump."
"Teleportation on the other hand, comes with a greater price. A great deal of spiritual energy known as 'anima' is required to fight the natural flow of the Lifestream and guide one's body and soul to a comparatively weak aetherial beacon."
"If one's body lacks sufficient anima, teleporting to a location may prove impossible. Luckily for most of us, anima is restored quickly and should not prohibit regular travel."

And connected to that, the in-game Help window on teleporting actually mentions about anima as well, although it does not actually refer to it by name:

"Unlike other spells, Teleport does not require MP to cast, but a type of naturally regenerating spiritual energy."

Additionally, not long after ARR's launch an official lore post by Camate in this forum clarified the situation: anima is the body's aetheric tolerance to teleportation, but not everyone has the same consistent 'anima level', some people have higher anima than others, with some having virtually none, thus this means those with low anima can only teleport a few times before needing 'to rest' compared to others. The player's character, by contrast, was mentioned as having a 'very high' anima level and so could teleport constantly with no ill effect (this was basically the explanation for the gameplay replacement of anima cost for teleporting with a cost in gil, the later written into the story as a tax used to pay off the high cost of rebuilding the aetheryte network after the original one was destroyed in the Calamity), which also works towards explaining also why pure-born Garleans cannot teleport as well by extension, as quoted below:

Why doesn't everyone use aetherytes?
To traverse the Lifestream safely with Teleport and Return requires a great deal of spiritual energy, known as anima. While many individuals, such as adventurers, possess the fortitude to endure such travel, some individuals do not. What’s more, even if one has the ability to use aetherytes, the frequency with which one can do so varies. In essence, for some, the recast time for these spells can be far longer than for an adventurer.

As a result, only a fraction of the populace can utilize aetherial travel habitually, which is why chocobos, airships, and other forms of transportation still play a major role in Eorzea.

Presumably this is also the core reason why Thancred in Heavensward and beyond can no longer teleport as well as pure-born Garleans not being able to teleport at all - he probably has virtually no anima at all now due to Flow stripping it from him, and pure-born Garleans have never had any significant anima to start off with.