Indiana Jones was sent to retrieve the Ark. If he hadn't gone, the Ark would not have been retrieved or they would have had to send someone else to do it but that doesn't invalidate Indy's involvement. He was recruited. It was his task.

He also didn't know if the power of the Ark was real and both the Axis and Allies seem to have been wrong about what the Ark does because Indiana only learns that the Ark is not to be disturbed in the course of his investigations. Hitler seemed to believe the Ark would make his army invincible and that belief was enough to make the Allies recruit Indiana to try to stop that from happening.

He brought it back as requested. If he hadn't, some other party might have claimed the Ark. And he was able to bring information about the dangers of the Ark which led to it being secured properly.

He obtained the Ark and he obtained knowledge.

And even if his involvement hadn't ultimately amounted to anything, its still justified for him to make the attempt. Sometimes stories can work even if the hero fails. Rocky lost to Apollo in the first Rocky movie but he achieved his personal goal of going 15 rounds with the guy.

But there's no plot issue. The movie was about watching Indiana Jones make a journey to many interesting exotic far off places and ultimately he did get the Ark and he did bring the information back to the military.

The thing to keep in mind too is that this is supposed to be a throwback to old movie serials and pulp comics.

Also, Leonard's rebuttal is not a plot problem either. He says Indiana was supposed to bring it back to a museum. But we're talking about an object where, if you remove the lid, everyone in the surrounding area dies. Do you want that at a museum? It was better that something that dangerous be secured. Its actually a classic story. The hero seeks some treasure or MacGuffin of power, then realizes that its better if nobody has it. Maybe the treasure is cursed or the artifact of power is too dangerous or corrupts the user or could fall into the wrong hands.

People change their minds. Look at Back to the Future. Doc changes his mind multiple times about the time machine and about knowing one's own future. The first movie, Doc lives because he changes his mind after Marty leaves 1955. He also thinks that Jennifer running into her future self could cause the destruction of the galaxy. All that happens when they do meet is they faint.

The Dragon Ball series begins with Bulma and Goku seeking out the Dragon Balls so Bulma can make a wish. But that story arc ends with Oolong wishing for panties to keep Emperor Pilaf from making his wish for world domination.

That's it. The whole journey for panties. But it didn't amount to nothing. Bulma and Yamcha essentially both get what they wanted to wish for when they started dating each other. The Dragon Ball radar Bulma made for this mission ends up being useful many many times in future stories. Goku meets Master Roshi on the way which will begin his ongoing training making him strong enough to fight an endless succession of threats. Goku got the Flying Nimbus. And so on.