There are things like Minio which lots and lots of people use as an S3-compatible object store because it's so simple to set up. Most S3 alternatives are just a part of much larger filing system that's more demanding to set up. NextCloud is pretty big as well, though I don't know the exact numbers.
I think in the end, it doesn't matter as much. These are meant to be deployed for a cohesive user base that numbers between a single geek and an entire region of a country or small org.
They most often use libre data formats and protocols to store and communicate data. In such a situation, the network effect is less pronounced, and measuring market share isn't as important. As long as the service works reliably and meets user needs, I don't think people will clamour to replace them with proprietary solutions.
It's rare that a self-hosted piece of software is not present on this list. As you can see, the coverage is pretty extensive.