For rapidplay do you mean half hour through an hour per side? I'd pick the same openings as a 3 hour per side with extra time added past move 40 controls. For less than half an hour that's when intuition starts playing a larger role. You could even get away with junk like the Hippo at under 30 minutes per side since white will be far better developed yet not find a viable way to open lines within that time (development matters because of how open the position is and access to weaknesses.) I mean he can but it will eat up some thinking time, and many will centralize rooks now and ask questions later.
Time Limit As An Opening Choice Determinant
I like the Hippo. Especially from a b6 move order. Interestingly black surrenders space and gains "time" from the point of view of our discussion. I always find that space is difficult to convert into a win with more limited time. This is relevant to the discussion because the first player has to "watch all the exits" but the second player just needs to get to one !
Something to keep in mind (also quite obvious, but not often made explicit) when talking about this is that while two openings may be given the same label of 'soundness' (ex/ being +=), the positions they give will often be avstly different.
So while I think rapidplay is still too slow to play an opening that can be refuted-or close to- by the opponent working through strategic considerations, taking them into a highly complex position that is objectively bad may be viable if it is likely to strain their time use.
So I would say an opening such as the englund gambit (1.d4 e5) would not be so good as white probably has time to avoid all the traps and kill off any initiative black can get for the pawn. However maybe a marginally sound line such as the danish, traxler counter gambit or blumenfeld could be very much more playable than in standard, as their lines are much more labyrinth like and will pressurise the opponents time in order for them to accurately avoi all the pitfals.
I'd like to argue something that is obvious but not always stated. Even so I think it worth discussing.
Given a long enough time limit, or correspondence play, I suggest that the best opening is one that is near absolutely sound as possible.
At a faster time limit , from the point of view of beating a human, his or her opponent is best taken in to territory they don't know. Perhaps this and the last paragraph are so obvious , that it's something not really touched on that often.
But what about time limits in between that of "Rapidplay" and "All day for one game" ?
I believe the evening leagues we have in Britain are more common than elsewhere. We play 30 in 1.25 hours and finish in 15 min (or adjournments). This is a strange time limit. Perhaps too fast for objectivity but not slow enough for just playing an "ambush" type of opening. So specifically we could talk about an opening that is moderately sound (for many of our levels) but has a little "ambush" potential.
More generally I wonder if it would be possible to quantify by objectivity~ambush potential other time limits with their opening recommendations (with the help of engines ?)
As an example, I reckon that after 1d4 b5 is a viable option with shorter time limits but not for a game that lasts a whole day...perhaps ? Likewise the same might be said of the Morra Gambit...perhaps ? By the same token I'm considering Marshall's French gambit for my evening league.
Too long a time control will allow "reflection" to triumph over an "ambush" strategy ...whereas for short time controls the opponent can counter objectivity by ambush ?
Thoughts ?