There is no way to make an unbreakable mast. If you could, you would not want the boat anyway. That having been said, masts range quite a bit in ability to take abuse.
In my life, I have owned a Dart 18, Hobie 14, 16,18 Nacra 5.8, Several Nacra 6.0’s and a couple of A cats. The Nacra 6.0 mast was the heaviest, but I broke 1 and bent 4 of them. These were sailed hard and mostly bent under extreme circumstances or abuse. The dart mast got the most abuse and it is still straight after 28 years. Heavy does not equate to bulletproof.

Personally, I think if you don’t abuse them, a carbon mast will last a long time, ditto with an aluminum mast. I think you need to do a reasonable amount of maintenance i.e. replace shrouds every year-18 months, and diamond wires every 2 years, wire tie the hound so the shackle does not loosen over time causing demasting, tie the boat down, don’t leave the sails up unattended on the beach, don’t pitchpole in 15 ft of water and you will be fine. If you want a true beach cat, as opposed to a racing catamaran, a carbon spar is probably not a good choice.
Maybe a F16 is too heavy to make a carbon mast worthwhile, I don’t know. It certainly would make it easier to right the boat for a light solo skipper (yes wout I know you can carry all sorts of righting aids also but they are a pain in the butt. I can right my a cat just by holding onto the dolphin striker and leaning back. I weigh ~ 165 lbs.
I certainly would not bother with carbon beams with that high a minimum weight. If the class lowered the min weight by 30 lbs or so, a carbon stick and beams becomes a more realistic option.

Cheers,
Eric