I think that what you're suggesting here is probably a lot more likely to be implemented by coinbase than the custom fee sends. Low/med/high is a great balance between control that everyone's talking about, and flexibility.
Don't forget that coinbase isn't actually a wallet. It is actually an exchange that lets you store funds on it.
Therefore, you don't have control over your private keys to sign messages. This is different to blockchain.info. The reason they were asking these kind of high fees were because of the high amount of unconfirmed transactions and everyone is trying to compete for a fast confirmation. So it's not just them that's setting the fee, it's basically everyone on the network that's sending transactions.
I am using Coinbase more than year but I do not find any option to reduce or increase fee volume. Now already mempool is seems empty so why you still need to bother fees as a matter here. Not only Coinbase all the wallet providers decreased their default transaction fee equals to eth gas fee.
This is a centralized wallet, if you read the FAQ page to learn the terms about the having the fund and reason for not sharing the private key then you could able to understand about it. Wallet such as blockchain and MEW got hacked many times but coinbase doesn't.
Now fees on coinbase has been reduced to 0.000015 btc for each transactions bro.