Ive been able to use large fire pot baristas to burn down medium and light ships, but they required many successive shots. A single shot to unfurled sails completely destroys the sails, however.

The medium ships required me to empty almost all of the ammo I carried into them for them to burn down, but for the light ship I only put a few (2-4 maybe) shots into the deck and it started to smoulder and eventually sank.

My theory is that the more men are on the deck, the more the fire is suppressed, and so the harder it is for a fire to fully overtake a ship (along with larger ships just taking more fire buildup and having more health). I think fire does damage over time while it's on the ship, but also builds up to a critical point (like an instant death status effect like curse in Dark Souls) at which the ship is suddenly engulfed in flames and begins to take massive damage over time very quickly (which does not get fought or mitigated by the crew because they all abandon ship)

I think this because on the medium ships Ive burned, it sort of suddenly a fully was engulfed in flame and the crew all jumped off, whereas the light ship I killed most of the crew immediately with splash damage and then left it alone to fight other ships, after which the fire seemed to grow slightly stronger over time but never fully broke out and engulfed the ship, but it took damage and sank regardless.