Fortified european cities caused a lot of troubled. Most Mongol siege victories in Europe where Pyrrhic, with massive losses that couldn't be replaced that far from their homeland.
They ended up controlling most of the Hungarian countryside, but almost none of the key fortified cities, the same in Croatia and other areas, rendering their gains useless, since forces could march out at any time from the multiple forces and strike them.
I don't know much about Mongols in Central Europe, so probably true: they were far away from the steppes, probably lacked siege machines, etc.
Also, in the lands of Rus' stone fortifications were a very rare thing - there's almost no suitable stone for contstruction, so most castles and fortresses were wooden, so they did burn.
None of the stone fortresses in the north, where there are suitable materials, were plundered, AFAIK, so you must be right.
They ended up controlling most of the Hungarian countryside, but almost none of the key fortified cities, the same in Croatia and other areas, rendering their gains useless, since forces could march out at any time from the multiple forces and strike them.