Yeah, there are pros and cons to both options, but I think the designers got it right this time as no player is able to produce more than 1 unit of JHI per year, which prevents spam and maintains their status as "uber-elites". Even if you make their training reqs higher (your preferred option), most players who can get to the stage of producing JHI at all would have the capacity within their empires to conceivably use 4 or 5 "safe" provinces just to build up for multiple JHIs. All you get then is a bunch of JHIs really late in the game when they don't matter.

They truly are a frightening unit to face on the field as they don't have any weaknesses whatsoever. They can be used for any hand-to-hand role you can possibly imagine. Even their relative costliness is mitigated by the fact that they don't get ground down in attrition fighting due to their absurdly high attack and armour piercing. The other guys will almost always die or run screaming for their mamas after a couple of "rounds" of fighting.