For the sake of clarity, I will divide my answer into three, which refers to the reasons why a samurai would commit seppuku (and why it's the "right" thing to do) - losing a battle, as punishment/to atone for a mistake, and to follow his lord in death.

For those that lost a battle, seppuku serves two purposes: one, he will avoid the possibility of mistreatment by his captors. And two, by dying in a most painful way possible, he avoids accusations of cowardice, thus keeping his honour intact.

For samurai that was ordered to commit seppuku (due to a crime, real or imagined), it is considered a more dignified spectacle; the ceremony is performed in private, viewed only by the select few. The alternative would be crucifixion or being burned alive in public, which would be deeply shameful.

And finally, the practice of junshi - following your lord in death - is seen as an expression of supreme loyalty, a way for a samurai to state "I only have one lord, and I rather die than serve another". But as you said - it's better to keep a good man than letting him die pointlessly - which is why the practice was eventually banned by the Tokugawa Shogunate in 1663.

tl;dr:

it's better to cut your belly than be tortured by your enemies

it's better to cut your belly than to be tortured by the authorities

it's better to cut your belly than be seen as "disloyal" or "fickle" towards your deceased lord

References:

A Brief History of the Samurai - A New History of the Warrior Elite (Jonathan Clements)

The Art of the Samurai - Yamamoto Tsunetomo's Hagakure - trans. by Barry D. Steben.

Also, why was harakiri so specific? Why did those committing seppuku have to disembowel themselves, which is a painful and inefficient way of killing yourself? Was slitting your throat or otherwise injuring yourself in a way they would kill you more quickly seen as cowardly? It doesn't seem like the intent was to cause pain, since under most circumstances the person committing seppuku would be beheaded shortly after gutting themselves anyway.