In Hollywood films, sieges typically involve a brief period of preparation during which the invaders make camp outside the city (and usually do plenty of dastardly things, as orcs/Mongols/baddies are wont to do), followed by an all-out march on the walls, guns-blazin - usually involving trebuchets, ladders, towers, etc.
Now, I understand that even in those situations when, during a siege, troops did directly assault the walls, they usually had quite a long time spent softening up the defense, starving them out, etc. And I understand that medieval armies generally just preferred to starve the defenders out and win by attrition. But, two questions:
When was it strategic to simply assault the walls - either as fast as possible, or after softening the defense up? When would a medieval commander typically decide that waiting the defense out (and receiving an eventual surrender without an actual confrontation) was not worth it?
Could you provide historical instances in which a siege of a major city/fortress escalated to scaling the walls pretty much instantly? Like (Game of Thrones spoilers) when Stannis the Mannis attacks Kings Landing at the Battle of Blackwater (and pretty much attempts to scale the walls as soon as he arrives, not bothering with the whole "starve them out" strategy).
I can't speak for medieval Europe or later times, but in Asia (specifically, the Mongols) they tended to use other tactics than simply surrounding the stronghold to weaken the people inside first. An example would be capturing the surrounding local villages and towns but letting the survivors run back towards the central stronghold - this meant that there would be more mouths to feed. You could effectively double the amount of people inside a stronghold by doing this, and from there it'd be much easier to take the city.
However, I can't seem to recall of any large siege where they stormed the walls - the Mongols managed to starve out most (if not all) of the strongholds they came across.
Other than the Mongols, there doesn't appear to me to be any major battle in Chinese/Japanese history where a siege escalated to storming the walls almost immediately (or for a short time after). The defenders either managed to whittle away the besieging army, had a garrison large enough to repel said army, or had a reinforcing army close by.
Spoilers for ASOIAF/GOT:
Stannis had split his army into two portions - the fleet, and the amphibious assault from the river. You have to think, his army numbered an odd 20,000 or so, compared to the 7,000 in King's Landing. Both his army and fleet outnumbered what was at KL, so the admiral person decided instead to go for a full frontal assault. In my opinion it was much less of a siege. A siege is where you effectively surround and cut off a town/city/castle's supplies. He did none of that.