Wouldn't the idea be that the user always sees 10mBTC no matter what, but the receiver may receive less if the user decides to pay with a huge transaction?

It may be acceptable that receivers don't always receive exactly what they requested, at least for person-to-business transactions.  For person-to-person transactions of course any fee at all is confusing because you intuitively expect that if you send 1 mBTC, then 1 mBTC will arrive the other end. I wonder if we'll end up in a world where buying things from shops involves paying fees, and (more occasional?) person-to-person transactions tend to be free and people just understand that the money isn't going to be spendable for a while. Or alternatively that wallets let you override the safeguards on spending unconfirmed coins when the user is sure that they trust the sender.