They did not trade the lives of eight people for the lives of one. They just used a squad of eight people to find Ryan and let him go home. This mission doesn't have to be dead.
During the mission to save Ryan, the squad accidentally supported the task of guarding the bridge. They died in heroic battles with the Germans, not simply in Ryan.
Ryan should be grateful for his whole life, but as a bystander, you can't put the death of eight people on Ryan. It was a remarkable feat that obliterated their singable sacrifices when they fought alone and the enemy who killed several times more than themselves.
Let's keep thinking about it, is Ryan really particularly important?
No, the squad was all killed precisely because Ryan wasn't that important.
If we replace Ryan with the president of the United States, the secretary of defense, Einstein, the atomic bomb expert... Will the squad choose to stay and defend the bridge?
No, they would choose to make the task of saving Ryan the highest priority, and immediately, take Ryan to safety.
It is precisely because Ryan's value is not higher than any of them, and far less than the value of defending the bridge, that they will choose to collectively support the bridge. The value of the bridge is higher than that of thousands of Ryans, so they put Ryan's safety on the back burner.
While he held his ground, Ryan was fighting. The squad's protection against Ryan is that as long as one of the squad members is alive, it will keep Ryan safe. But what if reinforcements don't come? What about reinforcements coming later? What if Ryan was killed too?
Precisely because Ryan is not so important, the squad's surplus sense of responsibility has led them to perform various side missions along the way and sacrifice for it.
Let's think again, the key point of the mission is not actually Ryan.
The most important significance of saving Private Ryan is politics, which means that we do not abandon any soldier in war. In this mission, saving Ryan is more important than saving Ryan successfully.
From the moment the eight-man squad embarks on a journey to save Ryan, whether it is to bring Ryan back unscathed, or to sacrifice all the members, Ryan is not found, or Ryan is killed, the strategic significance of this mission has been achieved.
If Ryan dies, the authorities can reply to a mother like this, "... Your son does not want to leave the battlefield, he is brave and fearless, and he holds the bridge until the last moment. It's a shame we can't bring him back to you, but he'll always be with us..."
Ryan is alive, and he's been living propaganda material all his life.
This remarkable mission had succeeded the moment Marshall ordered it. Ryan himself, on the other hand, was less important.
Ryan was only particularly important to his mother.