Playing NT, you get a 2♠ lead (4th best). Would you EVER play high from dummy with...
KQJx
opposite
9x
???
yes. for instance, if I needed to win this trick to score 9 cashers in two outside suits before they won their 5 tricks in the form of the ♠A and four in the last suit.
Yes it depends what you need. If you absolutely need 3 tricks then definitely duck, as the ten being on your left is more likely than ace third on your left by a lot (the holding that playing the king wins on). However, if you only need 2 tricks, and can't afford the loser, then play the king. Usually it will not always be clear what you need exactly, so you just have to judge each case on its own merits.