Does open source matter if you still depend on someone else’s infrastructure?

Been thinking about this after looking at different Discord alternatives. A lot of projects advertise themselves as open source but the community still ends up depending on infrastructure controlled by someone else. You can inspect the code or fork it but if moving your members, permissions, data and integrations is a nightmare, how much control do you really have? Self-hosting obviously gives you more control but running communication infrastructure for a large community comes with its own headaches. Curious where people here draw the line. Is owning the infrastructure itself the important part or is portability and having a realistic way to leave more important?