I always assumed he just learned English for the first time in the Shakesperean era and liked it, so kept the accent for fun. The fact he's two thousand years older than Shakespeare is fairly irrelevant if he didn't speak the language until the 16th century.
Sort of like the immortal bad guy Culp in Starman, who spoke English with a Cockney accent, which meant he was looked down on in society, so when he learned French, ensured he learned how to speak it like a refined gentleman.