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. © 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!
2, Exile a nonland card from your hand: Put four time counters on the exiled card. If it doesn’t have suspend, it gains suspend.
Thats the card text of Jhoira. You dont suspend any card and therefore you can exile any nonland card as you mention. Creatures, Enchantments, Artifacts, everything at instant speed.
Even the moment of casting them doesnt have any timing restrictions, because you are restricted casting them on resolution of the last time counter beeing removed. here from the gatherer site: As the second triggered ability resolves, you must cast the card if able. Timing restrictions based on the card’s type are ignored. (2013-06-07)
Jhoira of the Ghitu can suspend at instant speed, no matter if that spell would normally be castable/suspendable at instant speed.