I re-use yeast routinely.
My house, now over-run with wife and daughters, is always too warm to use English yeast so I routinely re-use US 05. You make a brew with the dried yeast pack and save up the empty 250ml Lemonade bottles, adding a good squirt of Star San.
Come racking or bottling day, two weeks in, leave a good amount of beer in the FV - say a litre plus trub. Then swirl it around and drop it into the bottles.
This whole thing has to be done very carefully and everything sterilised to within an inch of its existence. It does work, though and the yeast keeps well under the green beer for 2 or even 3 months in the fridge and does not need a starter.
If you ask - is it worth the effort for the cost of a new pack of yeast?
My answer is - it's my hobby and I like messing around with it to see what works.
BTW, I would only re-use slurry yeast like this for one "generation", even though multiple times. To my thinking, there is much less risk in reusing a slurry for 6 daughter brews than for 6 generations of brews.