Because the prison system and the mechanics by which it carries out its sentences are a public service so of course no one pays for the execution materials just like you don't pay for firefighters to put out a fire.

As for those 10 people who knows if they are actually innocent or not. Maybe they were released on a technicality or misinterpreted evidence, maybe they were 100% innocent. They are the only ones who truly know. Just because windmills or solar power plants kill a few migrating birds doesn't mean we should stop using windmills. It sucks that innocent people have to die but I think their (unwitting) sacrifice is worth upholding a system that has "worked" for us since the beginning.