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?