According to its wikipedia article, the Dragon 2 is powered by 8 SuperDraco engines. And according to the SuperDraco's article, each one of them can store up to 1,388kg of propellant at an Isp of 240s. Does that mean each engine has that amount of propellant? Even if I generously give the Dragon 2 a dry mass of 10t (e.g. including crew plus cargo), that would amount up to 1,7km/s delta-v. That seems to be quite a lot for a LEO-ferry. On the other hand, it is not enough for a moon landing. So what motivates this budget?
That's 1,388 kg of propellant for the whole vehicle, not per engine.
Reading the original document referred to by Wikipedia, it says 3,060 pounds of propellant for the Crew Dragon capsule.
(It's on page 8. The fuels are NTO and MMH and the combined weight of both is given.)
The Super Dracos are used for two purposes in the initial design.
Launch Abort System, and powered landing.
For LAS usage, they need to get away from an exploding booster, faster than the explosion wavefront.
For powered landing the ultimate goal is to let the capsule hits its aerodynamic terminal velocity and then finally brake in the last few seconds for a powered landing. Initial attempts (at least of DragonFly test vehicle) will be parachutes to reduce terminal velocity and then powered landing.
Their budget of thrust and time is designed around those two criteria. Using this as a Red Dragon (to Mars) is an interesting question as to how they will improve the fuel load for that mission, if at all.