Yeah, of course if catapults and heavy warships significantly outranged towers and forts, that would also solve the problem.
If light-medium-heavy ships were an upgrade progression, IMO the heavier ships ought to also cost more, to be realistic, but have good enough stats to be worth it. The concern is that civs without heavy warships might just lose control of the sea to civs that do have heavy warships. To keep that from happening too early in the game, the upgrades could be slow and/or expensive, and the benefits only incremental rather than overwhelming.
Although right now, sea dominance is backwards. Celts and Iberians - historically relatively primitive people, around 0 A.D. - have the best navies. Briton medium warships have more HP and carry more troops than triremes. Iberian fire ships are cheap and effective. The supposedly "naval" civs with heavy warships - Ptolemies, Carthaginians, Romans, and Seleucids - are actually no better than average at sea.