Speaking for git, you are correct. A git archive permanently records all commits. The idea being that you want both recovery and audit abilities.
As far as the git archive expanding to fill the universe, actually for most items that belong in a git archive, git manages to be quite space-efficient as the generations build up in my experience.
But, of course, for a number of reasons, you may not want to keep history forever, so yes, there are git commands that can reset the baseline and purge past history.
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