There are also known addresses with no private keys.
There are no addresses with no private keys.
Better formulation: It hasn't been proved that there's an address that has no private keys. On average, each one has 2
96 different keys.
There are addresses for which the possibility of there being a known private key is practically entirely impossible.
For example - these:
1BitcoinEaterAddressDontSendf59kuE
1CounterpartyXXXXXXXXXXXXXXXUWLpVr
1111111111111111111114oLvT2
The reason the private key is almost certainly unknown is these addresses are like vanity addresses. I own a 16 core (32 thread) Ryzen 9 5950 (Monero ASIC lol). This is one of the most powerful consumer CPUs you can currently buy, and actually stomps a lot of the Server type chips as well.
Executing the command
vanitygen 1BitcoinEaterAddressDoNotS
(Unfortunately I cannot even search for the last three letters) starts a search that on my chip is calculated to have a 50/50 chance of finding an address starting like this in:
74,159,994,000,000,000,000,000,000,000 years.
For a little (impossible) perspective the universe is thought to be only:
14,000,000,000 years old.
So... there are no known private keys for those addresses without some kind of backdoor for SHA2.
lol
I agree with you that finding one of those private keys is IMPOSSIBLE. But my inner AKCHUALLY needs to say the word practically in front of it not too be all itchy and scratchy inside.) 
