The primary benefit of having a Power Pool as a non-Manifester is access to Psionic Feats/Focus.
There are numerous abilities that only require Psionic Focus, such as the Deadly Throw and Deep Impact Feats among many others.
Some Psionic Prestige Classes only require a Power Pool, not a Manifester level, such as Phrenic Slayer. Most of these involve gaining Manifestation abilities, but Pyrokineticist gives other ways of using Power Points. The Mystic Archer requires a Psionic power but does not allow for spending Power Points.
Additionally, Unlocked Talent gives access to Powers (but also gives a ML of 1 so it doesn't really apply here... unless you are just looking for light access to Psionic without taking a Psionic Class).
If you use Wild Talent to take Psionic creation and Metapsionic feats, you are limited by the number of Power Points as to which Psionic items you could create (they are "spent" each day creating the item).
Maenad (and potentially other Psionic races) get Wild Talent as a bonus Feat and have a racial ability to spend Power Points.
Outburst: Maenads can dampen their mental processes for an increase in raw power called an outburst. As a result, they take a -2 penalty to Intelligence and Wisdom but gain a +2 bonus to Strength. The character must spend one power point at the beginning of each round during an outburst and may stop an outburst at any time.
The Sleeping Goddess Path of War discipline uses Power Points.
Note: You do not gain additional Power Points from Intelligence. This is a benefit to Psionic classes.
How To Determine Bonus Power Points: Your key ability score grants you additional power points equal to your key ability modifier × your manifester level ×½.
Wild Talent gives no "key ability score".
Benefit: Your latent power of psionics flares to life, conferring upon you the designation of a psionic character. As a psionic character, you gain a reserve of 2 power points and can take psionic feats, metapsionic feats, and psionic item creation feats. You do not, however, gain the ability to manifest powers simply by virtue of having this feat.