Please, never mind some of my opinion which I will first address about blockchain.com wallet
- It does not support segwit addresses, making its users to pay more on transaction fee. Nested segwit can reduced fee by 26% while native segwit can reduce fee by 42%
- Like you included in the OP board, it does not support replace-by-fee
- It is a web wallet, most vulnerable to attacks
- Can not spend unconfirmed transaction input(s)
These major reasons should discourage people from using blockchain wallet.
There are some other information that needs to be shared about child-pay-for-parent.
1. The sender if using blockchain wallet, he can still use of child-pay-for-parent if he has change address after broadcasting the transaction, the UTXO (unspent transaction output) which is the change back into sender's wallet another address after broadcasting the transaction, all the sender needs is to spend from the change address UTXO by including funds on the change address in another transaction and send the bitcoin into another own (sender) address, or maybe sending to another person, it will work also. But in this case, the fee should be enough in a way it will cover two transactions to be confirmed earlier, enough fee to cover child transaction, and enough fee to also add up to the parent transactions, which will be paid in the child transaction to get the transaction confirmed earlier.
2. The second case is what is well explained above, but this can only happen if the sender is sending to himself, or tell the receiver to do it. This can be done on wallets like electrum that can spend unconfirmed input transactions, this will make the receiver to spend the transaction into another address on his electrum wallet, but in case he wants to send part of the bitcoin to another person, he can also just use the opportunity, his confirmed transaction and the transaction he sent (to his address or another address) will be confirmed at ones if enough fee is used as explained above, but it should be noted that the receiver has to spend from the unconfirmed transaction input.
Lastly, on electrum wallet, replace-by-fee is by default, but it is not bad to check it as implied.