That's what a mining pool is. There is no other type of mining pool.
The purpose of mining is to find valid blocks to add to the blockchain. A transaction is "confirmed" when it is part of a block in a blockchain that has some number of blocks after it. The number of blocks after it is the number of confirmations the transaction is considered to have.
Don't mining pools concentrate on mining new blocks, as it's more profitable? Can't we have a mining pool with old ASIC/GPU miner that would do ONLY confirmations, and would do all confirmations, even those with minimal fee?
No that wouldn't actually fix it. There is a limit to how many transactions can be processed regardless of how many miners are running. Adding more miners doesn't actually increase capacity just the difficulty.
The way to fix this is increasing the size of the blocks, which is trivial from a technical standpoint, but it has some implications that the current majority of miners are not willing to accept.
The purpose of mining is to find valid blocks to add to the blockchain. A transaction is "confirmed" when it is part of a block in a blockchain that has some number of blocks after it. The number of blocks after it is the number of confirmations the transaction is considered to have.