In my experience they *do* make a different beer - that's the point ;~)
they believed sometimes a batch worked out to produce a better bitter (no nursery rhyme tongue-twister intended) & at other times a better 'best / special' was brewed - so the process was kind of seen as a best fit, given the constraints of plant, time & staff.
Do I think it's the best way to craft-brew individual beers? - No, ideally for me, you should brew distinct separate batches of beer, just as you would like them to taste (even this isn't an exact science though! - as nature makes changes to all of your raw materials).
But is it an authentic brewing method? Well, in a slightly different form, it goes back at least several hundred years. I've read that in Elizabethan times, children were given a fair amount of weaker 'small beer' made from the second runnings/washings of a mash, the first runnings having gone to brew a much stronger beer.
I've not heard of anyone one in the UK quite doing this method, but I think Anchor Brewery in San Francisco have brewed a lower ABV 'small beer' on the back of their barley wine. cheers MikeMcG