Privacy may improve security, but usually not. It is a sometimes unintended consequence.
If I want to tell you a secret, I will bring you into a private room. Now we have privacy. If someone wants to listen in on our conversation, they will plant a bug in that room, or listen through the wall. To remain secure, I must add security countermeasures to prevent the bugs from transmitting, or extra noise to make being overheard difficult.
Your ISP's DNS might be more private, but if an attacker can poison your ISP's DNS cache (it has happened to me on my ISP) you won't be more secure. It's more secure to use a hardened DNS service, which is usually not local. But yes, this could be a minor privacy concern with a big enough attacker.
Just because you add privacy does not mean you added security. Just like because you add security does not mean you have privacy.
So please be honest about the motives for things like this. If you want more privacy, say so. Don't say it's a security problem when it's not.
If I want to tell you a secret, I will bring you into a private room. Now we have privacy. If someone wants to listen in on our conversation, they will plant a bug in that room, or listen through the wall. To remain secure, I must add security countermeasures to prevent the bugs from transmitting, or extra noise to make being overheard difficult.
Your ISP's DNS might be more private, but if an attacker can poison your ISP's DNS cache (it has happened to me on my ISP) you won't be more secure. It's more secure to use a hardened DNS service, which is usually not local. But yes, this could be a minor privacy concern with a big enough attacker.
Just because you add privacy does not mean you added security. Just like because you add security does not mean you have privacy.
So please be honest about the motives for things like this. If you want more privacy, say so. Don't say it's a security problem when it's not.