By "controls," I mean the situation whereby an ace is worth two controls, and a king one. Given four aces and four kings, there are 12 controls in all.
If two partners have 31 (random) high card points between them, they are favorites to make 6 NT (35 points for 7NT). Therefore, if partner opened a strong 1NT, I would, in theory, raise to 4NT with 15 high card points (quantitative), asking partner to go to 6NT with 17 or a good 16, and pass otherwise.
One obvious danger is that even if a partnership has 31 points, it will still go down if the opponents have two aces, and may go down if they have an ace and king, particularly of the same suit), within their nine points. That's because the opponents have four and three controls, respectively, leaving the declarer with only eight or nine. The declaring side should have at least 10 controls to go with their 31 points (off only one ace or two kings) to bid 6NT.
So I would be happy to raise 1NT to 4NT with a 15-pointer like the following:
♠ Axx ♡ Axx ♢Qxxx ♣ AJx. This has six controls (more than my "fair share" of 4.5). Even if partner had all the remaining "quacks" (queens and jacks), it would be impossible to have 16 points without at least 3 controls, and nearly all 16 point hands would have 4.
On the other hand, there is only one control in this 15 pointer: ♠KQJx ♡ QJx ♢QJx ♣ QJx. Even with "17," partner could be off two aces. So I would be reluctant to raise to 4NT with this hand. In fact, I would prefer to raise to 4NT with a slightly weaker version of the first hand (remove the jack to reduce the point count to 14, but maintain six controls): ♠ Axx ♡ Axx ♢Qxxx ♣ Axx.
Is my concern about controls reasonable in this instance?