Kayn is a very balanced champion, or arguably a slightly above average jungler. He is completely capable of hard carrying if you know what you're doing. By all means try him out, and don't let the choosing forms thing intimidate you. When you get experience with Kayn, it's a painless process. These are the questions I ask myself when deciding which form to go with:
Which form will be easier to obtain based on the enemy team? If the enemy team has 3 melee or ranged champs, this point isn't too big of a deal. But if they have 4 or more, then you will either have to go out of your way to fight someone or delay a major power spike.
How much crowd control does the enemy team have? While both forms of Kayn are vulnerable to crowd control, assassin Kayn is especially so. He will just get insta popped before he has a chance to ult. Roots and grounded effects are particularly annoying for Kayn, since they disable his entire kit except for his W.
How tanky is the enemy team? This is an obvious point. If the enemy team has more than 1 person that builds defensive items, I would consider that a tanky team and a point in Rhaast's favor.
What does my own team need? In most cases, a team will value the cc and survivability Rhaast brings. But sometimes, your team already has the frontline department covered and needs an assassin to take care of the backline.
How fed did I get in the early game? Overall, Rhaast is the safer pick if you fell behind since he's still useful with his cc. But assassin Kayn is better at snowballing an early lead thanks to his great map mobility and burst.
After asking myself these 5 questions, I'll only pick shadow assassin if it is favored for at least 4 of the questions. You should honestly consider Rhaast as the default transformation, while shadow assassin is the niche pick. As for Kayn's ult, it's only a death sentence if you used it incorrectly or were going to die anyways. But you are correct, its main use is the un targetability that allows Kayn to wait for cooldowns. Keep it mind that the ult is also a useful tower diving tool. Being Rhaast kinda makes this ult unconditionally amazing from its damage and healing alone. Well, I guess the one condition is that you use it on a tank. The long range in assassin form makes it a reliable chasing tool, but the short range on Rhaast may require you to use it preemptively if you're trying to chase with it. Also remember that the assassin ult resets his passive, which is critically important for extended skirmishes since Kayn's damage is pretty underwhelming without it.
