One of the reasons why galleys have remained the oldest warship to date was due to the nature of warfare on the European continent. Because the most dangerous enemies of the European kingdoms of the early modern era were all concentrated around the Baltic, the English Channel and the Mediterranean, it thus made sense to use vessels best suited to shallow channels and fickle winds that could becalm larger ships.
A basilisk galley carries some of the largest guns known to Christendom, and is instrumental in battering fortresses down with its monstrously huge gun. However, despite this, basilisk galleys are rather weak on their own, have a poor reload rate and also have the same range as a fully-upgraded stronghold, and so they cannot be fully relied on to take apart enemy fortifications on their own. You must have Bombardment researched before a Basilisk Galley can be produced.
Because of the size of the basilisk and the relative underdeveloped technology regarding broadside-mounting warships, it was thus more practical to use galleys for the job of transporting huge guns and firing them. Once larger ships and more destructive guns found their way into the hands of navies worldwide, however, the galley's apogee came to an end and it was delegated to coastal patrol duty. Galleys have been used in the American war of independence and during the 1805 campaign against Denmark, but the dismal performance of these oared vessels ensured that those were the last time galleys would ever be used.