Snipers intentionally shoot to not kill sometimes, so they get more targets.

That isn't allowed by the Geneva convention. It is very effective though, so I'm sure it is done.

If your country is invaded, would you care about Geneva convention?

You make it sound like it is intentionally done but if the shooter is far away/has poor accuracy and the soldier has body armor, chances are he will be incapacitated but not killed. After that the question is: is more morally ok to killed the downed soldier or wait for his unit who is still and active aggressor.

Yeah, intentionally is not allowed, you are supposed to try for a clean kill. Doing so is as you point out difficult.

Interesting I would have guessed the opposite. Why?

Because the hurt suffer a lot. Getting through life missing a leg is not pleasant. Also dozens risk their life saving a down but alive friend, while you will leave the dead until it is safe

The number one objective is to not become another injured person or body that needs to be handled. You always take cover first then decide next moves.

Kill the sniper. Don't fixate on casualties. Slice the pie, identify probable locations, send teams to neutralize the threat.

Take cover and throw them a rope.

I suggest watching Full Metal Jacket.