Just speaking for myself, after decades of growing, you wont catch me flushing soils and depriving my plants of nutrients in the last weeks of life, no siree.
I'll go ahead and cut back on nutes, go strait water often the last week or so because economically there is no reason to keep pumping them in at that point, but the plant is none the wiser to what is going on.
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You could rinse that soil till the cows come home, it will still be good healthy soil.. all I've done by flushing is created a mess and threatened to drown my plant if it doesn't behave.
Flushing is for trying to fix accidents.. PH, over nutes etc.. and even then it oft does more harm than if you just let the plant ride it out (Unless you really let PH swing dramatically or over nuted them so badly they are just going to die).
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That's my take on it, everyone else's own mileage may vary.. I've lived through 4 decades of harvests (well, some years more than others) and have tried just about everything under the sun when it comes to flushing/not flushing..
I've never noticed a single difference in flavor (nothing worth noting) between flushed and not flushed everything else equal.
What I have noticed when I DO flush, side by side with sisters I don't flush, is towards the end the ones who are not flushed have filled out much more aggressively and still spout out a few white hairs even at the end.
All anecdotal.. all just one guy rambling.. everyone else's mileage may vary..