Calling with MMSI is supposed to be the modern way to call. However it is little used by sailors or by at least one captian I am friendly with who runs a large, high tech cruise ship
I have used it a few times to raise ships and once Bermuda Harbor Radio when I could not get their attention on channel 16
On most radios it is clumsy to enter the number, but OK once you have entered and saved a frequently used one.
Calling by MMSI works very well, since the recipient's radio screams or rings LOUDLY. It will get me in from the cockpit to our bleow-deck radio when the engine is running.