At least when it's self-hosted, it's your responsibility and you can fix it. When you are anything larger than a tiny company, this is much less risky.

Remember that 'the cloud' just means 'someone else's computers' so you are subject to their infrastructure management practices and uptime guarantees (or lack thereof).

Even for a company much larger than tiny, you're better off with GitHub from a reliability perspective. Most medium companies (up to hundreds of employees) do not have operations staff anywhere near as responsive as GitHub's are.

Look at their status history. The vast majority of companies could not boast such a record for their internal operations.

Not to mention if it's one person who decided to set up the self-hosted solution and then that person leaves. How reliable is it then?

Someone else you pay to keep data safe, up and running to do continuous integration in this particular case.

(Almost certainly) less load, more control over the hardware it's running on.