I am just pulling numbers out of thin air.
Assuming there is a 1% chance of a bad batch.
And that by “bad” we mean, that 100% of the batch fails.
If I buy just one batch, my chances are 1 out 100 to lose my pool in a mirror.
I only need one bad batch to lose my pool.
If I buy two batches, one bad batch is no problem. Two bad batches would be a problem. But the chances of getting two bad batches is 1% * 1% or 0.0001%.
Does that sound right, or am I missing something? Probability calculations were not my strong suite in math class 
For mirror you only need two brands, since you can lose half of it.
But yeah sure, for RAID you could even protect yourself from “concurrent bad batch failures probability” by using more brands. If you would use 4 different brands, a whole batch could go wrong without you loosing data in RAIDZ2 8-wide.
Then you would get the same security against bad batches as with mirror.
Or to look at it from a different angle, I assume that after 7y of usage, a single batch has a pretty similar failure rate. If I buy 8 Seagate drives and we leave out the initial bathtub curve, it is unlikely (at least in my experience) that one drive fails after one year, the next after two, and the next after three. More likely, the will fail all in year 7 (just an arbitrary year).
So it is less about when they fail (because they all will fail one day) but more about how concurrent they fail. And by using multiple batches (two for mirror and four for a 8-wide RAIDZ2) you can protect yourself from that.
From a home lab perspective I think it is unrealistic (at least in my country) to get a good deal on 4 different brands. Even two is sometimes hard to pull off.
Of course one of the main question is, how realistic is it that you get a “bad” batch? 1%? 0.000000000001%? I don’t know either.
I don’t have hard numbers, but stories like this from @Stux tell me it is more likely than it might seam at first glance: RAIDZ3 vs 3-WAY Mirror - #6 by Stux