SQLite is fine right up until you want concurrent writers. Once you need multiple users, cross-host access, or anything that looks like shared infra instead of a local cache, the file-locking model stops being cute and starts setting the rules for the whole design. For collaborative versioning, Postgres makes more sense.
For a distributed VCS, what would be the need for such things? Even if it were a really big project, how many writes could be going on that this becomes a bottleneck? I don't see it but maybe you have a situation in mind.