Earlier quoted context omitted.
It is possible. I've been running my own for a year, but it takes quite a hefty server at least with Synapse, and it's not cheaper compared to the quite nice 5 euros a month pricing here. If you want to give it a try, this is what I used: https://github.com/spantaleev/matrix-docker-ansible-deploy
You can run Synapse on a cheapo VPS for <$5/month; it doesn't exactly require much.
Hope I could go with Conduit at some point.