What is the single biggest advantage of a memory palace over just repeating a list?

It gives you the items back in a fixed, correct order — and lets you jump to any position — because the route itself encodes the sequence.

Rote repetition is fragile: drop one item and the rest scramble; you also can't easily recall "the 7th thing." A palace fixes both. The order of the loci is the order of the list, stored for free by the geometry of a place you already know. You can recall forwards, backwards, or jump straight to the 7th locus. Nothing to lose track of — the building remembers the sequence for you.