What kind of hand is best for a Jacoby 2NT call, rather than cuebidding, considering the Response Structure to Jacoby 2NT and the possible problems with a cuebidding sequence?
The "ideal hand" seems to be a balanced hand with "primes," with "primes" defined as Aces and internal suit honors (A-K-Q of trumps). These are hands that often need pattern from Opener (coverage of xxx on the side, for example), and Quantitative Bash is OK when Responder has all suits controlled. Thus, consider Kxxx-Axx-Axx-Axx or AQxx-Axx-Axx-xxx. In either situation, Jacoby 2NT would work wonders.
You don't always have primes, though. What factors might lead to use of a Jacoby 2NT sequence instead of a cuebidding sequence?
On factor might be slow values in the other major. Hands with KQxx, for example, in the other major are difficult. You often cannot bid or do not want to bid that major as your first call, which will result in a cue from partner biding "Ace or Shortness," which is not really that helpful. This is a problem situation, with Jacoby 2NT often being the best course.
Another factor might be a troubling minor-suit option. With, for instance, Axx/xxx in the minors, bidding one, planning to support Opener's major at your second call, will induce a cue from partner that might be the King, or Ace opposite xxx, but it might also be the Queen. That does not help much. Similarly, with Qxx in a minor, you might cause a problem because partner cannot cue a stiff here, what you may want to hear. Thus, with Ax+, xx+, or Qx+ in each minor, you might be better of with a Jacoby 2NT start.
So, a Jacoby 2NT start seems best when Responder has one of the following hand types (always balanced or semi-balanced, it seems):
Primes and a space
Primes plus slow values in the other major
Primes plus minors that are each Ax+, Qx+, or xx+
Primes plus any two
Primes plus all three
The idea, however, is to think through likely auctions and plan accordingly. If you have a desire to describe your hand, then one course might be best, as opposed to a desired to ask what partner has.
Consider holding AKxx-xxxx-Qx-Axx or AKxx-xxxx-Ax-Qxx, after partner opens One Spade. These seem very similar, but they are not. Consider likely auctions.
On the first, suppose that you bid Two Clubs, planning to raise spades at the next opportunity. It would be tremendous if partner could bid Two Diamonds, right? Now, you can bid Two Spades, setting trumps. Partner will clearly bid 2NT (poor trumps), and you can cue your diamond Queen by bidding Three Diamonds, bypassing Three Clubs to also deny two top clubs. When it matters, partner will cue Three Hearts, and you can cue Three Spades to show two top spades. When it matters, partner will cue Three No Trump, Serious, and you can complete your picture by showing the club control (Four Clubs). Excellent auction. The auction is similarly easy if Opener rebids Two Hearts instead, or Two Spades, or whatever.
On the second, life is more difficult after Two Clubs. The auction is identical up to a point, but you cannot cue Four Clubs. You gain nothing by starting with a cuebidding sequence. Plus, any call by Opener that bypasses your ability to set trumps at the two-level will deny any ability for you to clarify whether you do or do not have a club control. Partner may bid too much thinking that you must have the Ace or King for your initial call. Jacoby 2NT might be better.
So, although the hand types described for good Jacoby 2NT considerations are rough guides, it still seems that planning, meaning auction prediction, is key.