Absolutely. We'd like to support GitLab and Bitbucket next but had to pick a starting point and GitHub was an obvious choice. If there are other providers you think we should pursue, let me know.
What about sr.ht, savannah.nongnu.org or self-hosted projects using cgit or gitea frontends, most of which lacking such integrations the likes of gitlab and bitbucket provide? I'm sure it's more difficult to support things like these, but I'm wondering how flexible the system is with regards to this.