Yes, Janissaries are good vs total morons, such as the AI. However, you can kill the AI with pretty much ANYTHING easily. They die easily to concentrated fire, flanking, anything from a later era, and are every bit as vulnerable to ranged bombardment as other units. They are good, but they are not game breaking.
Any unit you're using for extra sight, no matter HOW you are supposedly using it, can see 1 tile further still as USA. There are NO civs that can "loosely simulate" it, and when you're playing against something with an IQ above 50 or so, it is very helpful. Sometimes it is even helpful against the AI, as if you need ANY uniques there.
"nigh unkillable" is a total joke. You get caught by a knight in the flatlands, and you lose almost all your hp, and another one shuffling in can kill you. As you ap
proach, your str can be cut down by archer type units, navies, or cities easily, making it hard to actually finish something off. Attacking a fortified unit on forests/hills isn't going to be favorable either - you'll be largely even against earlier things like longswords/knights (which don't get D bonuses but don't take the flat penalty there) and opposing muskets, subject to who can actually manage a surround on the other player. On defense, you'll probably get kills easily, but on offense against anybody competent, it won't be so easy to move in.
It is a strong unit, just as it was in civ IV. However, just as it was in civ IV, its benefit is mid game, where the American UA and most other civs' UAs/UUs/UBs have already been having an impact for much longer. What if you're fighting horse on horse vs an american player? You don't think it matters if he knows where your forces are even while you can't see him? Keep dreaming.
I'm not saying America is a top civ, just that it's ridiculous to put it behind a civ with such a flagrantly awful UA.
What your failing to see (get it ?) is that when you enter an opponants territory he will see you regardless thus he will have better sight than you but you will have only slightly better sight than a non-American civ. On defense your sight bonus is useless because you can see everything within your boundaries anyways. In an even straight up fight the Jannissary has more real benefit than the extra seeing and moving American counter parts.