What would chess openings be like without castling and/or the double pawn move? Chess has a fairly elegant set of rules, but it has two rather ugly "rules hacks" in it:


Pawns can move two squares forward, but only on their first move, and have the rather ugly rule of en passant to get rid of the nasty side effect of having your 5th rank pawns get bypassed.
Castling lets you move two pieces at once, and has a bunch of rules about when you're allowed to do it.


Now, the usual justification of these is that they make the game go faster. According to this question, the two-square pawn move was introduced because players would begin each game with 1. e3 e6 2. e4 e5 (or similar). Castling was a variation on the "king's leap" many chess variants had. It makes a certain degree of sense--games are meant to be fun, and why not get to the action more quickly?

On the other hand, chess theory has advanced a lot since the 1500s. In modern opening theory, black often forgoes immediate center pawn moves. 1. e3 would likely meet the reply 1... Nf6, not 1... e6. It stands to reason that some of the considerations then may no longer be the case.

So, has anyone ever done any studies into what chess openings would look like without castling, without the double pawn move, or both?
Overall, the game would be slower and opening attacks would be more aggressive at times.
The purpose of implementing the double-step was to speed up the game. That way, those pesky pawns wouldn't have to waste so much time, i.e. moves, moving forward to mount an attack or to develop an area of advantage/control. But with the double-step gone, we would have to revert back to the slow way of the ancients.
The double-step is often done on the c and f files to let the knights out without blocking the pawns. Now it would take more time to flesh out that plan, as it would now take two turns to let the knight out onto its most advantageous opening square.
In some semi-closed positions, the double-step is used as an immediate can opener. However, having to move the can-opener pawn two times might give the opponent just enough time to react and defeat, or at least nullify, your attack. A few more draws might result because the position stays closed.
Additionally, in some games, the double-step is used to quickly advance a rook pawn, and break open the enemy's king's encampment. But with it gone, a single step must be done, thereby giving the opponent time to react. Have a look at the below position and deduce for yourself how this affects the game.
 [FEN &quot;3r1r2/1bp3k1/1p1qp2p/p2p2n1/5NQ1/PBNP2P1/1PP4P/1K2R2R w KQkq - 0 1&quot;]

As for no castling, it would also lead to a slower game, but at the same time lead to more aggressive opening attacks. The concept of castling, even if the move isn't allowed anymore, would still be a popular motif due to how it keeps the king safe.
Doing castling manually takes several moves, and with both players doing so, games would start to be several moves longer. Due to the slow process of doing so, an opponent may try to catch the king in the act and take him down. Kings would be in the center longer, also leading to a reason to favor, and as such an increase, in open positions. That allows for an attack to be done faster. Artificial kingside castling would increase in use due to the process taking much longer than on the queenside.
At the same time, however, with the hindrance of the double-step, such attacks may be also seen less often due to the need to spend time mobilizing pawns. The enemy might use your time to manually castle, ruining your plan.