My god, the things I've seen in repos. vim .swp files. Project documentation kept as Word documents and Excel spreadsheets. Stray core dumps and error logs in random subdirectories, dated to when the repo was still CVS. Binary snapshots of database tables. But the most impressive by far was a repo where someone had managed to commit and push the entirety of their My Documents folder, weighing in at 2.4GB.
(I checked this out the day before I left for vacation, so to be fair, my research might have not been thorough enough to find each and every implementation - but I think it is comprehensive enough to make some preliminary judgement)
I highly recommend git-annex. It is like git-lfs but a bit less mature but much more powerful. Especially good if you don't want to set up a centralized lfs server.
Binary files don't cause the issue, but because binary files don't deltify / pack well significant use of them makes repos degenerate much faster.