There weren't any city sections or facilities in the ancient times which you could use to ease your defeat of your opponents
What about water supply and grain houses? And harbors to cut off the rest of the supplies? I agree with what you're saying on the whole, but this strikes me as a bit fishy.
I suppose such stuff could matter if the city in question was large enough, but huge cities were a rare occurence in ancient Europe. Water supply was mostly natural - since most cities were built along river banks - and food stores were likely to be organised in very well defended places as at some point the besieged folk also had the angry starving citizens to contend with. I think you're overestimating the infrastructure of ancient cities. Rome itself was an exception at that time, not a rule, and its most glorious form would be considered a large city even in modern times.
A naval blockade was a given if an important supply line went through the water. You didn't need to control the harbor to cut off the supplies. Most of the time, however, there simply were no supply lines. Keep in mind that most of the Rome's enemies were rather isolated communities - and even if they were part of some kingdom or empire, ancient logistics and means of communication often meant that the defending party had to fend for themselves. When it came to more powerful local states Rome often subdued them through diplomacy and powerplay rather than through flashy and incredibly costly sieges to the enemy's capital. Carthage's destruction shouldn't be considered in any way a highlight of the Roman way of doing things and IIRC the fact it was completely destroyed was due to internal Roman politics, not due to necessity or any rational benefit.
Also, continuing to defend a siege after a part of the city fell would be a truly desperate measure and, contrary to hollywood productions, people had common sense and if surrender would increase chances of survival, they would often do it. Both Roman and Greek histories are full of cowards, turncoats, overly ambitious traitors and people who don't want to die and will do whatever it takes to keep on living. When reading some historical accounts I often had the feeling that for a modern, post-nationalistic man it's much easier to relate to pre-nationalistic ancient people than to our forefathers who died in meaningless trench battles a hundred years ago.
Romans were building proper PR for sieges for centuries too. Back when they were subjugating the Italian Peninsula they built quite a naughty reputation among the hundreds of locals tribes and communities. If they surrendered immediately they would be spared, if they would struggle they would be decimated, and prolonged resistance could prompt the Roman army, depending on the consul leading them, to burn the place to the ground and slaughter all who weren't lucky enough to run away. It shouldn't be a surprise that most of the locals opened the gates and disarmed themselves as soon as it was apparent that the Romans are coming.
