> I'm not sure why Presidents were given the ability to pardon.

Because of the impossibility of law written in advance perfectly covering all cases and to provide a mechanism for correction of overpunishment that cannot be effectively anticipated in crafting general law. (That's more the reason why the traditional power of chief executives seen in state governments and the British government they were all more or less modeled on was retained when a federal executive was created; the US Constitution was very much not create ex nihilo in a historical vaccuum.)

> Besides corruption, bias, or self-interest, nothing else can come out of it.

Every viewpoint is "bias" relative to every other viewpoint, so that piece is a nullity, but it is certain;y not the case that corruption and self-interest are the only impacts or motivations for applying the pardon power.

Which isn't to say that there aren't arguments for putting more guardrails around the application of the power by the executive (or perhaps just radically changing the nature of the federal executive, to improve the application of its powers generally and not just the pardon power).