Take the recent Lichess downtime, for example. Their main server had a hardware issue that required physical intervention. This meant the site was down for over 10 hours, and there wasn't much they could do except wait for OVH to send a tech.
If Lichess had been on AWS, the provider would have automatically moved their workload to a functioning server, and the outage would have been much shorter or possibly avoided altogether.
For Lichess, a non-profit, this tradeoff still make sense. Their service, while important to its users, isn't critical. Nobody dies if Lichess is down and the cost savings help them keep running. But if your business can't afford downtime, the extra guarantees from a public cloud provider can definitely be worth paying for.