Binding outsiders is often described as an extremely powerful, or even game-breaking ability. But it is not exactly cheap. Why is it regarded as so powerful? Are there specific ways it gets used such that people consider it to be so powerful, and what are they?
Planar ally and planar binding are actually a pretty decent microcosm of several classes of Pathfinder material that are traditional routes to abuse.
They are open-ended, but have enough rules that players can leverage.
This allows players to get clever and mitigate the costs and/or risks associated with these spells, dramatically amping up their value to the player. Directly converting player cleverness to value means that if you are clever enough, you can be more powerful than you should be at your level. Most things in the game do not reward player cleverness so directly, meaning there are limits that keep even clever players at a certain strength appropriate to their level.
And, with the internet, we can replace cleverness with a Google search.
It’s worth noting that it is crucial here that the rules are not just “the GM figures something out,” because then there is nothing for players to leverage or abuse. It is by giving some rules, but a lot of ways to get at them, that these spells get into trouble. Of course, “fixing” this problem by either making things less open-ended or just leaving everything up to the GM have their own problems—the former inevitably eliminates a lot of options that we would expect from a setting like Pathfinder’s, while the latter leaves the GM with frustratingly little help in deciding how things should go.
They expand constantly; every new extraplanar creature printed is a possible candidate for planar binding or planar ally.
While Paizo of course attempts to prevent “power creep” (having new material be more powerful than old material, meaning that buying a new book powers up some characters), they (and, to be fair, just about every RPG publisher ever) are far from perfect in this regard. That means every book is the opportunity for a new “mistake” to add something overly-powerful to the options for planar ally or planar binding.
They give players access to monster abilities.
This is the big one: monster designers tend to think in terms of GM use. They think about how the monster will serve as a foil to the PCs, a challenge. They often neglect to consider what will happen when a PC gets access to the monster’s abilities. That means that “mistakes” as discussed in point 2 are much, much more likely to happen.
It abuses several of the game’s “economies,” particularly the action economy
Characters in Pathfinder are limited by several scarce resources, like spell slots or actions during a turn. Planar ally and planar binding can give you many, many effects for a single spell slot, from the spell-like abilities of whatever you call, and then it also gives you an entire extra body with its own set of actions, doubling the amount of things you can accomplish in a single turn. Action economy abuse is up there with monster-ability abuse as one of the most tried-and-true ways to break the game.
You may note that this checklist, aside from #4, also applied to polymorph effects in D&D 3.5, and is one of the main reasons why Paizo completely overhauled polymorph effects in Pathfinder (easily my choice for the best work Paizo has ever done). However, planar ally and planar binding have changed little from how they worked in 3.5.