I have heard that argument before, it's simply based on the fact that mining pools operate and can operate without any regulations , license or KYC of any sort, so most mining pools won't be forced to handle information regarding their clients, so think about it this way.

A fresh block > miners, this is a single transaction which says pool xyz sent x bitcoins to abc and that's all about it, so even knowing the mining pool that created that output you can't do much with that information, unless the pool hands you the information of that miner such as their IP address, total hashrate and other addresses they might have used on the same account.

With exchanges however, since most of them involve the use of fiat money wether to buy or to sell crypto, they are subject to regulation, exchanges that require no KYC will soon be history , we saw how binance turned around recently, it's just how things are, if you own an exchange and want to operate freely worldwide you will have to obey the rules of  world (more so the U.S law).


But then, under some circumstances, regulation can get to mining pools as well, the government can even access the pool's server with court warrant, a less "democratic" government can detain the pool's owner/s' and force them to hand out those information, so mining to a pool isn't really as "private" as most people think.

With that said, there are still better and more secured ways that ensure better privacy, using a good mixer makes your coins a lot harder to track than mining to a mining pool.