A very obvious case would be people sending email - spammers are always hunting to find ways to get their traffic out from IPs without reputation problems. They'll send email from this service and then the services IP addresses will become blacklisted - or more likely the underlying service provider will kick them out to protect their IP space.

That's just the most trivial issue, though, and can be part way resolved by host blocking outbound in 25. You'll also get botnet C&C, hosting of illegal content, use to mask scanning traffic, etc. All of these are sometimes operated by people who do not have a problem with ephemeral services and will happily automate creating new accounts and setting up new "temporary" servers. Using github for authentication will partially help as github no doubt has mechanisms in place to limit automatic account creation, but I'd only trust that so far.

First, it can cost way too much money for the service to be sustainable. Second, it opens up many liability issues. Third, your upstream provider can stop the service when they feel there's any kind of a problem at all – even if you work for Amazon.