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do you mean something that would automatically update the backup when a file is changed on disk?
bup currently doesn't do that. but there's been some talk of using inotify or another such method of knowing exactly which files are modified when they are so that bup could instantly work on those.
in theory it should be feasible, it's not implemented yet however
backuppc is a mature technology and can very well be trusted for collecting backups.
there are some areas in which bup is trying to innovate in order to change how backups are considered (storage size being one of those)
true. and actually bup can't use git's tooling directly because of the different use cases it's optimized for. git won't make any use of bup's optimizations: midx (combination of multiple .idx files into a handful of bigger ones to reduce page faults during binary searches) and bloom filter.
git's tools, namely filter-branch and gc have been reported to work on limited-size bup repositories, but it very quickly eats up all ram and cpu and never finishes because of the sheer amount of objects that are usually stored in a bup repository
some ppl have already started working on this and there's been activity on the mailing list lately about this topic.
however it's a dangerous feature to add in (backup tools should never screw up their storage, and this feature goes and removes things) so a lot of care is needed.
the boring answer is: it's coming, and we need a lot of help for vetting patches and testing them out.
as is the case with most 100% volunteer-based free software: lack of time and/or ppl to help.
There are currently multiple interfaces available to bup, but each one has some quirks. bup's web interface is still very embryonic and would need the magic touch of some designers / integration specialists to make it fun to work with.
currently bup doesn't implement encryption (since it's a pretty hard feature to get right and we do want to finish coding other key features -- like old backup removal -- before we get to that)
some ppl have reported using an encrypted storage backend like ecryptfs to store their bup repositories in. that option shouldn't be too hard to put together.