Well the responsibility falls on the infrastructure people in an open-source project as soon as you self-host. But then again many open-source projects already do this. I'd rather have control over my repositories than host them on someone else's server which is why I'd go for self-hosted Gitlab or Gitea.
This has been my point which I have made for self-hosting over the last few months since GitHub was down on a regular basis, and going against locking in their ecosystem, which is another risk. GitLab cloud is no different. [0]
Running applications at scale is hard but running Gitlab in a low traffic environment is incredibly stable and low maintenance.
This sounds to me like you've not really bought in to the peripheral software project tools Gitlab offers like boards, issue tracking, CI/CD for running tests, etc. In which case, Gitlab seems a bit like overkill. Running your own git remote is pretty straightforward.
Github is great, but when it's down, it impacts developers in many places.
When we spread our eggs across many baskets, we are more resilient.