I don’t have exact numbers, but a large portion of Discourse instances is run as managed hosting, by Discourse.org, Communiteq.com, and maybe some other smaller players.
It is true that a managed hosting provider will normally not give customers console access. A provider cannot reasonably take responsibility for the security, stability, and maintenance of a system it does not fully control.
However, that does not mean customers do not own their data. Of course they do.
Some of our customers occasionally open a support ticket asking us to run a rails c script. We review the script for security and sanity, run it, and provide the output when requested. The turnaround time may be slightly longer than running it yourself, but in return you get an additional sanity check at no extra cost.
With managed hosting, you don’t need to worry about performing updates, because that is handled for you. Also, urgent security updates can usually be deployed quickly, without each individual administrator first having to notice the issue and take action.