Jhoira of the Ghitu timing restrictions question

I don't see what prevents Jhoira from effectively suspending any card at instant speed.

I understand that the rules for the suspend keyword mean that you can only suspend a card if you could cast it at that time - so you can't suspend a creature at instant speed. From searching the internet, it seems that people ascribe the same restriction to Jhoira - that you can not, for example, suspend a creature on your opponent's end step. But I don't quite see why not.

The text on the card just says (a) that the cost is to pay 2 mana and exile a non-land card from your hand. (b) then it gets 4 time counters. (c) then is gains suspended.

So at the moment you exiled a creature, you would just be paying the casting cost. It would only gain the time counters and suspend triggers once its in exile. Based on that, it would seem you could in practice use Jhoira to suspend anything at instant speed - which is pretty OP.

I am guessing there is some good answer showing that my reasoning is wrong - I'd appreciate any insight!