The President's pardon is a political tool the chief executive has in their arsenal which allows them to check the power of the judiciary. If an innocent defendant goes through the judicial system and is convicted anyway then the President may issue out a pardon to exonerate them. This is the ideal use of the pardon, but in reality it is used to benefit the lackeys of the President or the governors who can issue out pardons on the state level. Because the de facto use is not consistent with reason or civil governance, given its arbitraity, I believe there needs to be more restrictions on that particular power.
In the theory of checks and balances, one branch can check the power of another, however, there is another theory which is separation of power meaning that one branch cannot obstruct the power of the others. This sounds contradictory but it is not. For a check to not be an obstruction the check needs to be a negative on a power and that negative can only be an active reaction. There are several checks which violate this rule, one being the power of the President's veto. The veto does not have to be an active check on the legislature since a bill from Congress needs to be signed by the President in order to be enacted. This means that the President can passively do nothing and still check the power of the legislature. There is a specific circumstance where if Congress is in session when the time frame to sign it ends then the bill will become law even without the President's signature, but that isn't all the time. To follow the two theories correctly, all bills will be able to become law without the President's signature but if the President objects to a bill then he can veto. This will force the President to be more active when checking the power of Congress.
Likewise, a pardon is just the veto against the judiciary. The judicial branch exercises its power to convict a defendant and the President may intervene to nullify that conviction. The pardon is an active check, which is consistent with the theory, however the timing of the pardon is not so. Just as a bill needs to complete its course through the legislative branch before the President may veto it, so to must a conviction pass through the entire judiciary before the President may pardon it. This means that a defendant must make an appeal all the way up to the Supreme Court before a Pardon may be applicable. The pardon should have no affect with the decision of the court, only to exonerate the individual defendant.
This way the theories of separation of power and system of checks & balances is better defined and implemented with reason and the power of the executive to be used inappropriately, that means arbitrarily, is restricted.