Shortening the rope

Because it's how you say "perform this sequence of operations atomically". The most recent example I happen to have seen is in the XSETTINGS spec where it notes you need a server grab at one point to avoid a race condition, but just in general, X is all about multiple apps working in parallel on a bunch of shared state, and sometimes you need a locking primitive.

It's also used for various hacks (e.g. if your wm does rubber-band resizes, it'll grab the server to prevent other windows redrawing themselves over the rubber band, apps that want you to enter a password will sometimes grab the server to prevent shenanigans, ...).