We can and we did, they are implemented in AoE3 where they belong.
The unit was officially formed in 17th century, says so right in that link you keep posting.
Late 16th century isn’t given any context, at best was something irregular.
But if you really need actual medieval bomb throwers I’m sure there’s something much less anachronistic.
Like ceramic pot filled with greek fire of naphtha used by Byzantines, middle easterners, Indians and so on.
And I am sure China had explosive devices that you could throw too.
From gameplay perspective I am not a fan since there already are onagers and scorpions to give splash damage.
Also it probably would be broken unit on the closed maps, especially when massed which shouldn’t be too hard with a barrack unit.