Then later with the Pirates of the Caribbean movies that had included a CGI character with a heart problem 10 years after "Dragonheart"!

I think it's bigger than that. In 1973, The Three Musketeers came out, and a mess of other swashbucklers followed. After Star Wars, fantasy-adventures came back in full force. In the 80's and early 90's there was a wave of "swashbuckler" movies, Dragonheart would be at the tail end of that phase.
1981: Dragonslayer, Excalibur, Clash of the Titans
1982: Ivanhoe, The Scarlet Pimpernel, Conan the Barbarian, Beastmaster
1983: Nate and Hayes, Jamaica Inn, Deathstalker, Krull
1984: Conan the Destroyer, Sword of the Valiant, Master of Ballantrae
1985: Red Sonja, The Corsican Brothers, The Black Arrow, Legend, Ladyhawke
1986: Pirates, Highlander
1987: Masters of the Universe, Lionheart, Princess Bride
1988: Willow, Deathstalker III
1989: The Return of the Musketeers, Sinbad of the Seven Seas
1990: Shipwrecked, Treasure Island, Cyrano de Bergerac
1991: Robin Hood: Prince of Thieves, Hook, Merlin of the Crystal Cave
1992: Army of Darkness, Last of the Mohicans, Odisseya Kapitana Blada (Captain Blood)
1993: The Three Musketeers
1994: Guinevere, Revenge of the Musketeers
1995: Cutthroat Island, First Knight, Braveheart, Kidnapped, Rob Roy
1996: Dragonheart, Return to Treasure Island, The Dark Mist
And on TV there was Covington Cross, Robin Hood (1984), Return to Treasure Island (1986), Hercules: The Legendary Journeys, and Xena: Warrior Princess.

I remember the first time I saw a tv spot of this, I thought it was "Hercules: The Legendary Journeys" film when Draco was seen fighting Bowen(he looked like the hydra from the show a bit until he started talking and my jaws dropped like "cool")!!