IMO, by far the majority of mover issues others attribute to inadequate "size" of the battery is simply down to knackered batteries. As the Prof and others have said a battery yielding adequate amps, here power, to start up and sustain a mover has nothing to do with the energy, Ah, "size", the holding capacity of a battery, just its ability to yield enough of the varying currents, for long enough. Also as said, the "energy" Ah, most users need to cover their mover demands, is a very small part of the energy a healthy battery of circa 80 plus Ah should hold.
I for well over a decade used a "traction" battery, of just 60Ah labelled capacity.
These are of course absolutely the ideal of those of the LA battery technologies, exactly the battery for traction duties, as powering a mover is.
Mover makers specifying minimum Ah capacities for their products are not in stating that portraying an understanding of what their product needs from the battery; I am sure they do actually understand, they just know if they say a high Ah there is every chance, given where their clients will buy a "caravan" battery from and what they get as a battery , it is going to do.
Further, it is a fact of life of two similarly knackered batteries, the bigger the holding capacity one will yield both proportionally more power and energy than its smaller sibling, The real life outcome is the individual with the biggest "size" knackered battery is not going to complain as early as one with a smaller battery. This and the fact the duty a mover asks from a battery is a very telling "test" of the battery's health; by quoting a girt great size battery the mover maker is buffering itself well away from users being unhappy with their product, even though the actual cause of that dissatisfaction lays elsewhere.