I suspect the Brewer's Friend advice is there to ensure that new brewers don't have any problems.
My average-gravity ales ferment out in about 4-6 days, then get a 2-3 day warm rest and 2-3 day cold crash, so it's unusual for them not to be kegged/bottled by the two week mark.
Kegs are ready to go once the finings settle (I try to hold out a full 3 days). Stored warm, bottles typically carbonate in less than a week. If you fill one plastic bottle, you can at least roughly monitor the pressure building and watch the yeast flocculate.
Once a beer is at that point, time and temperature are the enemy. Ideally I'd try to *finish* drinking a batch before it hits 6 weeks in the package, but that doesn't always happen. As long as your sanitation and oxygen pickup are good, beer shouldn't go "bad", but fresher is usually better.