That may be all well and good ... (and Boeing, like all manufacturers with any sense, will give advice with a keen eye to their own potential liability) ... but I suggest that the value of the earlier recommendation lies in picking up gross flight by flight errors.
A similar philosophy/technique often is employed on freighters with on board CG systems ... there is invariably an error of some magnitude ... but, for the crew, this error is more or less predictable more or less most of the time ....
What the crew ought to be looking out for is those occasional times when the apparent error suddenly changes with a degree of significance. Sure this might mean not much at all - but it could just save your neck if you elect to get the ginger beers to check it out prior to departure.
I can recall a couple of occasions where a VERY relieved crew gave thanks to the training system which had indoctrinated them in this sort of checking regimen with both fuel and CG calculations.
I may be a bit of a dinosaur but I strongly adhere to the credo that the more the technical complexity and reliance on computerised systems, the more there is the odd likelihood of (especially) software glitches causing subtle problems which can bite pilots on the tender parts without much warning ... the wise pilot keeps as many options as possible open to protect him/herself .... and uses whatever reasonable techniques are available to give the crew an edge over the machinery's foibles ..