Peak shape carries as much information as peak area does, and a badly tailing peak or a shouldered peak is telling you something about the sample or the column that matters.
System suitability checks on replicate injections of a known standard establish whether the method was in control — if the peak area varies by more than two per cent between replicates, something is wrong.
Detector linearity is why a heavily loaded peak can give false purity by compressing the main peak height while leaving impurity shoulders unchanged.
Inter-laboratory studies using identical methods on identical material show precision well within half a per cent when the method is locked down, pointing to method variability as the primary source of disagreement.
I would caution against over-interpreting small differences between runs, because the noise floor of the method is larger than most people assume.
If two labs give different numbers, the method difference is the first hypothesis, not lab quality.