Different Fortifications Against Raids Versus Sieges
The earliest fortifications were likely to have been primarily meant to defend against raids rather than sieges as very early (Mesolithic or Neolithic) warfare seems, in as best we can tell with the very limited evidence, to have been primarily focused on using raids to force enemies to vacate territory (by making it too dangerous for them to inhabit by inflicting losses). Raids are typically all about surprise (in part because the aim of the raid, either to steal goods or inflict casualties, can be done without any intention to stick around), so fortifications designed to resist them do not need to stop the enemy, merely slow them down long enough so that they can be detected and a response made ready….
In contrast, the emergence of states focused on territorial control create a different set of strategic objectives which lead towards the siege as the offensive method of choice over the raid. States, with their need to control and administer territory (and the desire to get control of that territory with its farming population intact so that they can be forced to farm that land and then have their agricultural surplus extracted as taxes), aim to gain control of areas of agricultural production, in order to extract resources from them (both to enrich the elite and core of the state, but also to fund further military activity).
Thus, the goal in besieging a fortified settlement (be that, as would be likely in this early period, a fortified town or as later a castle) is generally to get control of the administrative center. Most of the economic activity prior to the industrial revolution is not in the city; rather the city’s value is that it is an economic and administrative hub. Controlling the city allows a state to control and extract from the countryside around the city, which is the real prize. Control here thus means setting up a stable civilian administration within the city which can in turn extract resources from the countryside; this may or may not require a permanent garrison of some sort, but it almost always requires the complete collapse of organized resistance in the city. Needless to say, setting up a stable civilian administration is not something one generally does by surprise, and so the siege has to aim for more durable control over the settlement. It also requires fairly complete control; if you control most of the town but, say, a group of defenders are still holding out in a citadel somewhere, that is going to make it very difficult to set up a stable administration which can extract resources.