From years of reading early Medieval world history, one thing that sticks out to me is how many ancient cities that were once the equivalent of metropolises today were replaced by different cities mere miles away by the Arab Caliphate. It isn't unprecedented in history, but especially in Europe, south Asia and east Asia, it seems more likely for conquerors to take over cities rather than abandon them after conquest.
Is there an explanation for the trend of the Arab Caliphate quickly taking over territory and founding their own cities in lieu of settling around the political and economic foundations in the preexisting conquered cities? The three cities in the title are those that jump out at me as exemplary examples of what I am thinking about.
Its not really true that this is emblematic of the Islamic conquests, at least, not more so than other conquests of the period. Cordoba, Alexandria, Tunis, Isfahan, Bukhara, Merv and Sevilla are all examples of cities which formed some of the most important bits of the Islamic empire but were thriving, important cities beforehand too. Cordoba, for example, had been the capital of Roman Hispania while Merv and Bukhara had played a vital part along the silk road for centuries.
The reason several new cities were founded like Baghdad or Fustat vary depending on the city but it tends to be that the areas with the most new cities were depopulated when conquered. Lower egypt was heavily populated and thus the centre was maintained at Alexandria, however upper Egypt, ravaged by poor Byzantine administration and plague, had a low enough population that it was easy enough just to build a new city - Fustat, and then later Cairo. This was repeated in parts of Syria and Mesopatamia - left depopulated by war, plague and famine, it became easier to build model towns than reform the old near empty ones. This was especially true as the empire began to export Arabs across its territory to govern - they needed a place to stay and half the time it was easier to just give them a new town.
Baghdad is different - Ctesiphon was still thriving in the 8th century, so why build a new capital just down the road? Essentially, it was about prestige and power. A custom built capital could show the world the majesty of your empire and could be made to fit the new ruling structure perfectly - no need to jam mosques and towers into an old city when you can build a perfect one to show off. Its the same reason Peter the Great discarded a perfectly functional Moscow in favour of St. Petersburg, or why the early Americans settled on a small patch of swamp in Maryland rather than an already large city like New York or Boston. Baghdad became the model Islamic city and attracted people from around the world, built in a perfect circle as an homage to euclid and stocked with libraries, mosques and markets to spare. Why wouldn't you want this perfect city as a capital?
Finally some other new cities were built as garrison towns. As the empire moved away from using Arab soldiers and towards Turkic slaves it became increasingly obvious that coexistence between unruly, slave soldiers and regular citizens would prove difficult. The slave mamluks which made up the majority of the army were unruly and rude, so new cities were built which they could have to themselves so as not to disturb the empires citizens. The most famous example was Samarra, but that went pretty horribly wrong and had earth-shaking consequences.
TL;DR - the reasons vary from place to place but could have been either for prestige, to repopulate decaying regions or to house unruly slave-soldiers.
P.S Tunis is actually an ancient city, though it was called Tunes in classical times. It was honestly just chance that it got rebuilt rather than Carthage - both were ruins when the Arabs found them.
It wasn't just done by the Arab Caliphate. This has happened several times in history, including with Iran's current capital, Tehran. Tehran was once just a smaller town near the bigger city of Rayy, but after several centuries of growth, Tehran absorbed Rayy. This was the case with Ctsiphon and Memphis, though on a quicker scale.