The strongest justification for Richard III's actions was the risk of another round of civil war breaking out due to weakness and conflict in a regency government.
The traditional practice in a regency was to separate the offices of Protector and Guardian. The former exercised royal powers in the King's name, while the later had physical custody of the King and oversaw his upbringing. This division protected against abuse of power by the Protector by making sure the King was beyond the Protector's reach and free to sign off on a change of regency. However, that very division was dangerous when the government wasn't stable, since it provided ready made focuses for rival factions which could not easily displace each other without a civil war.
By pushing aside the Woodvilles and seizing the guardianship of Edward V and Richard of York in addition to the Protectorship, Richard of Gloucester removed a major potential source of instability.
But as Protector to a King who was only a few years away from majority, Richard of Gloucester had a Lame Duck problem. His ability to trade favors and set up the kind of long-term political relationships needed to keep England stable was limited by the universal knowledge that someday not too far away, Richard of Gloucester would have to step down in favor of Edward V. The normal solution here, a gradual hand-off of power to the young King under supervision of the Protector, was risky because it was incompatible with the close physical custody of the King inherent in preserving the outcome of the coup against the Woodvilles. So instead, Richard found a legal pretext to declare Edward V, Richard of York, and their sisters to be bastards and exclude them from the succession.
The next problem was the risk that a rival faction would raise rebellion in Edward's name. If Richard was responsible for his nephews' deaths, it was to eliminate this problem.
The problem Richard III couldn't solve was the risk of a rebellion or invasion in favor of another rival claimant. Henry Tudor was beyond Richard's reach, the Duke of Buckingham was too powerful to take down without a civil war, and Edward IV's daughters were too numerous to either arrange plausible accidents for all of them or keep them all under close custody, especially after the political fallout from the confinement and subsequent disappearance of their brothers. Ironically, Richard's actions earlier (the coup against the Woodvilles, seizing the throne, and the perception that he'd murdered his nephews) gave him a very weak air of legitimacy, pissed off a lot of people, and required him to pay off his inner circle for their support in ways that pissed off even more people, leading directly to Buckingham's unsuccessful rebellion and the successful Tudor invasion.
If Richard's action had succeeded in creating a strong government and putting a firm end to the Wars of the Roses, you could make a good argument that they were justified. A handful of murders to prevent another round or three of civil war is a pretty good tradeoff from a cold-blooded utilitarian perspective. But he failed, and in hindsight his actions may actually have been counterproductive on this from.