Yes, that would be true if the local storage were all hardware raid and running a raid 5 or faster, I guess. But one of the servers are only using single disks since it only supports software raid, and another server has slower SATA drives in a raid 5 array so it's not very fast either. The last server has a raid 5 SAS Array which probably would be faster than an IP SAN.
But it's not the only reason for getting one. Another reason is availability. If all VM's reside on an external storage, it's easy just to add it to any hardware in case of "emergency" (or maintenance). I'd rather depend on a high end SAN than on backups made nightly to a low end NAS 
Also backups will be faster than today since the network speed multiplies by 10.