Invulnerability is not a good game mechanic and is not fun to play against
Imo Invulnerability is a bad mechanic for this game as it prevents you from doing anything against a champ once it is active. At best you can cc the champ until this invulnerability wears off but you still can't kill them. You pretty much have to wait out whoever has it or somehow make them use it in a way that won't get yourself killed and then try to abuse the cooldown the only problem is if you somehow make the enemy blow this cooldown they will often just recall and play safe till the ults back up.
What spurred this current topic of conversation was champs like kayle, trydamere. Both these champs are unfun to play against any time they are strong and even when they are weak due to their invulnerability. Taric I believe is a bit more tolerable; however, that may be just because there is a decent delay. I feel invulnerability if anything should always have some form of delay on it or is gated by some other mechanic that can be countered when the ult is activated ie kayle being stunned in someway cancels the ult. trydamere i personally don't know how I would gate it perhaps it activates automatically after a certain amount of health
Now when I say invulnerability I do not include things such as zhonays as that is an item everyone has access too. I am simply referring to champ mechanics.