Khazaria alone has more than 100 cities according to Bavarian Geographer (IX century). Even if we assume that this is an overstatement (and it is), there are a lot of other sources that confirm the existence of big cities of Khazars, including archeology. And I am not talking about their tributaries, but about actual Khazar cities.
Itil – the most famous Khazar capital appears as a big city in Muslim sources. There were at least three big quarters according to Al-Masudi and Bek Joseph (ruler of Khazars who have correspondence with Andalusian Emir advisor Hasdai ibn Shaprut). Ibn Hawqal mention that Itil have more than 10000 Muslims and 30 mosques – this is another overstatement, but there are too many sources about Itil that confirm its big size. Ibn Hawqal also mention, that most of the Itil buildings are made from clay, wood and felt, but Khazar ruler owns a palace made from bricks. There were also churches, synagogues, baths and huge markets with merchants from different countries.
There are even more interesting examples like Sarkel fortress - Constantine VII Porphyrogenitus mentioned in his works that this fortress was built for Khazars by Petronas Kamateros, one the imperial officials. This fortress was built entirely of stone. Romans built it for Khazars because they were their allies against Abbasids that time.
There are many more Khazar cities, especially nameless ones (found by archaeologists), but I will not list them all. The point is that the Khazars had many cities, and quite large ones. This is not Baghdad or Changan, but these cities were not inferior to the cities of settled people. And that is only Khazars – another Turk and Mongol nomads also have big cities. So, nomads absolutely should have cities or castles.
As for the game mechanics – I think powerful nomadic ruler should be able to found cities, temples or castles in some baronies, but with big limitations. Most of his realm should remain steppe holdings. And if his county collapses this city must be converted to steppe holdings, because of other nomads plundering or because people just leave it in fear of being plundered (powerful rulers no longer protect them).