The only time that I've gotten a dry or burnt hits on my subtank is from when one of the legs of the cotton wasn't actually pushed down far enough to suck up juice. One side was fine but the other side wasn't. It worked fine for about a day, and then all of a sudden one hit was extremely harsh. However, I vape very light, I don't chain vape much if at all anymore.
As to the OP's question, when you get a burnt / dry hit, Yes, you'll need to change the wick at the bare minimum if it was a strong enough hit and it continues into subsequent hits like you described. If you catch it really early in the hit and stop sometimes you can simply figure out why you're getting a dry hit and rectify it without rewicking although we're talking about less than a penny and a few bits of your time to pull out the wick and stick a new piece of cotton in there so might as well just rewick it.
As far as replacing the coil... I've had both. One that no dry burning and dowsing in water would get rid of the burnt acrid taste and the coil had to be replaced, and the other time where dry burning the coil and dowsing it in a cup of water got rid of the bad taste and smell. But then again, a coil is a few pennies to produce and only a little bit of your time to do so not a big deal at all if you do need to replace it. It's those pesky prebuilt $4.50 coils that might give you a burnt hit on the 3rd hit you use them that are a drag to have to throw away.