I don't know that they do, but it's common sense. It might not be an option if an ILS is unmonitored due to the tower being closed. In that case I would be satisfied with some secondary system to cross-check the ILS (GPS, LOM, VOR cross-fix, etc). I think most, but not all, ILS's are monitored by the TRACON who will clear you for the approach.

Monitoring is just another layer of aviation redundancy...the more of those you take away the shorter you lifespan is going to get.