It is almost unanimously agreed upon that impact factor is a flawed way of assessing scientific output, and there are a lot of ideas on how this could be done better. None of them have taken hold. Publishers are mostly a reputation cartel.

Clarivate does control it because they tend to have the best citation data, but the formula is simple and could be computed by using data freely accessible in Crossref. Crossref tends to under report forward citations though due to publishers not uniformly depositing data.