If you track through a compressor, the compressor will be reacting to things that you will be cutting out further down the line. Sometimes that can sound strange.
It helps wind noise on outdoor gigs.
You can add more gain on the preamp because you won't be eating up headroom with low end you aren't going to use.
There is nothing wrong with using a high pass filter after the fact, but there are some advantages to cutting at the mic. Mostly because of where it is in the signal chain.