I am confused by this sentiment. Wouldn't moving to another product (like bitbucket or gitlab) put you in the same boat (since they also offer free private repositories)?
https://about.gitlab.com/pricing/
The free tier is the functionality you get for private repos. Public (not internal) repos get Gold capabilities.
Runner limits can be eliminated if you host your own runner to hook in to.
The above is specifically for GitLab.com hosting. Self-hosted is a different story with features.