Mobile cities are a common sci-fi setting. They are a staple ingredient in novels like "Mortal engine quartet" and "The inverted world"
Plot set aside, what justifies mobile cities on land? Giant excavators are real machines which can be used as such. Still, examining them reveals some flaws:
large footprit (track print), i.e. it leaves in its wake a smothered natural habitat. This was frequently mentioned in Mortal engine quartet. The smothered lands the tracks left behind were named "the hunting grounds".
difficult to maintain. Replacing Large metallic chassis parts that corrode involves hard work. Indeed, One of the mobile cities in the novel was built haphazardly.
guzzle lots of fuel when moving
may still be dependent on land-based farmland, hence the need to plan trips ahead of time.
may need traffic control, similar to that of ships. This is where a caravan of smaller units, or even motorhomes ("private" houses) may prove more useful, as they may use existing roads and traffic control.
cannot handle all terrains.
Repurposed ships, aircraft carriers and cargo ships may solve most of those problems, but the question was narrowed down to land-faring societies: Would mobile cities be practical or justifiable enough to be so appealing? Do they have an advantage over classical nomadic societies?