Advantage of SAN over a NAS storage that is mounted to a device? One of the reasons that we use SAN is to make it appear to the server as if it were local. What is the advantage of a SAN over a NAS storage that is mounted to a device?

A SAN appears as a raw block device and can do the things that a block device can but a filesystem can't. Two very common cases include data storage where an application is using the block device directly (as some databases can), or to serve as a boot volume for a diskless server (some servers and blade systems can speak iSCSI from firmware well enough to treat a SAN device as if it were locally attached long enough for the OS to get up and running).