While you are probably right, I'd let my players do it if they used a higher level spell slot. I just love it when they do these totally unexpected things.

Note that casting PFaD can cause an evil water weird to revert to good. So casting it on water not necessarily meant as drinking water to affect a creature that dwells in it is not unprecedented.

It's also not clear why the pool is briny. It's perfectly possible that one could purify the water around an elder brain only to find it "re-brined" after some suitable time, if it's that the elder brain is secreting $stuff.

Also note that versions of brine are used as components of food. What would happen if you cast purify food and drink on pickling brine containing pickles?

@TimothyAWiseman You can drink pickle brine (and many do). It doesn't need to be purified. Which raises the question of is the vicious brine of an elder brain potable :)

@Szega Do you have a source for that?

@NautArch "A water weird loses its evil alignment if its waters are cleansed with a purify food and drink spell." MM 299

That'll do it, @Szega!

This is a great answer but I guess that means most DMs will not allow it. I guess the other way to go about "cheesing" this boss is by using repelling blast until it's out of the pool

@BaconHero Even though the spell does not seem to make provision for casting at a higher level, you might be able to cast it multiple times, or ask your DM about casting it with a higher level slot to increase the volume of water that is purified. But I like your repelling blast idea as well. :)

@KorvinStarmast I added some language around upcasting.

Nobody said that it's the brackishness of the pool in particular that sustains the elder brain. It could be otherwise nutrient-rich maybe removing the salt is irrelevant to the brain.

'Elder Brain Brine! Perfect for adding that pep of flavour to your hapless prey! Get some from your nearest Illithid-Mart (Aisle three)!'

I mean maybe an Illithid janitor comes by every couple of days and casts Purify Food and Drink on the brine

"anything larger than 5' won't be able to be purified." -- well, a 5' radius sphere of it WOULD be purified. This strictly conains cube 7' on a side. So if you have a 100' x 100' by 50' pool, a mere (15*15*8)=1800 castings would purify the entire pool.

Oops, it should be 5.75 foot sided cube (did 2sqrt(5^2/2) not 2sqrt(5^2/3)). So 100' by 100' by 50' requires 20*20*10 = 4000 castings of purify food and drink to cover it. In any case, you should consider if leaving the water completely is fatal, maybe purifying some of it is damaging.

Also, who says the brine is nonmagical?

Could a DM rule that it causes some limited amount of damage to the Elder Brain to reward creativity without breaking the game?

@jpmc26 A DM can rule however they'd like on any action. I personally wouldn't rule that it does anything. It's 1st level spell against a CR14 monster's lair. And there are too many unknowns as to how the Elder Brain interacts with the brine. That, and the whole issue of just not enough volume (regardless of the Water Weird bit...although a Water Weird is Large, and PFaD basically covers a 10' diameter which is the whole water weird, so that may explain why it works.)