Aqua - here's the way I look at it and how we do things in my partnerships. I would also assume this with an expert partner that is up to speed on 21st century methods.
Opener's hand is broken into four separate categories.
1. A total POS. Bad controls, and I might have been passing a SF forcing 1N response if I were balanced. This hand does not cue bid over 3
♥. It does not make a NS try. It signs off. This says to partner, "I have a minimum and lousy controls. If you move past game, do so at your own risk".
2. A useful minimum. This is what NS was invented for. Opposite the right 17, or the right 5 or 6 loser hand, this hand type has potential. I'd say the hand tends to have a high loser count, but good controls, but this needn't be the case. Something like Ax KTxxx xx AJxx is right, even though it clearly does not have 'extras'.
3. Extra values. This is normally defined as an A or a K more than #2, but this isn't a hard and fast rule. The OP hand squarely fits within this definition. If one makes a serious try, it does not automatically force to slam. With the OP hand, I would feel very unlucky if slam was not at least fair if we had sufficient controls in the off suits and enough keys. I do agree that 6 ace is useful in this sequence.
4. The nuts. This hand will cue bid, and may be close to a slam force. It may take control, or it may hope partner does. In either case, it is extension of three.
By the way, I'm guessing you would not make a NS try with Ax KTxxx xx AJxx, if you would with the OP hand. I would kindly suggest that you've simply incorporated NS as a "hand that doesn't want to force to slam, but a hand that wants to show extras". Many bridge players in So Cal still play that a cue bid in a GF auction 'shows extras', and you are now casting these hands into NS auctions. But this is not how it is played in the mainstream. A NS hand just shows a minimum, and "I don't hate my hand".
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The partnership is better placed already by the serendipity of not having opened 1NT. South's range, thus far, is still 12 with 4-card support for clubs up to just short of a 2C opener.
What the heck does this mean? Did we imply we were balanced at some stage?