In our ideal world, everyone has all the free software in the world at their fingertips, installable through well-maintained, secure, and up-to-date package managers.
In the world we live in, there are rueful jokes for more than one programming language about installing some package manager in order to install another package manager, and the same holds true for operating systems.
The easiest way to run even simple single-user software is, indeed, often on someone else's computer, in particular if someone has gone through the trouble of writing a web-based interface for that software.
Then when we get to complex and collaboration-enabling software, often the only feasible way is shared computing infrastructure.
No, running software on someone else's computer is not the full control that we deserve of anything important to our lives, but having this software be free to potentially run on our own (or somewhere else) is orders of magnitude better than not.