IIRC it as invented to get the rooks out on the board quicker. Normally, it takes like four moves to properly get them out there (1. move pawn out of the way, 2. move rook ahead, 3. slip rook out through the side, 4. move rook onto the board.) With castling you can greatly reduce this if you've opened up the middle already.
I'll counter that, I read a couple of Go books and I'm still not clear of when the game ends or how you count points, go is very elegant but let's not pretend all its rules are simple and clear.
The game ends when both players pass. That's very simple and clear.
You score by counting the number of unoccupied points in your territory and adding the number of your opponent's stones you captured, + the "komi" that the second player gets to make up for going second (usually 6.5 for a full size board). (A common technique is to place all the stones you captured on empty points in your opponent's territory, so that you're subtracting the number of your captures from their territory). The only possible ambiguity there is around what constitutes territory; if you like then as a beginner you can just make the rule "unoccupied points in regions surrounded entirely by stones of your colour", which will make for a few tedious turns at the end where you fill in the last few gaps but won't change the scoring at all.
The rules are simple and clear – their consequences are not.
The game ends when both players have passed in succession. Each player may pass whenever they want. That's it. It's super clear. Figuring out when you can safely pass? That takes years of study. But essentially it is a strategic decision, not part of the rules. You can pass throughout the entire game, it would just be a really dumb strategy.
Regular players make counting points more advanced than it has to be in the interest of speed (similar to how mental maths tricks can be very advanced ways of computing simple sums or products).
The score is determined by the number of pieces you can put down on the board. That's it. (From this follows, of course, that empty intersection your opponent has solidly surrounded is probably not going to count toward your score because your opponent can kill whatever you try to play in there.)
Especially with the modern variants in play in competitive games, such as en passant capture and the like. Many fairly enthusiastic chess players aren't exactly sure what all the rules are.
Not counting online games, I've played many 100s of games of chess with many dozens of people, mostly strangers, incl 12-year-olds (when I was 12) and not once did a dispute or difference of opinion arise about the legality of any move (incl en-passant moves).
What is the name of this strange country where players who are not just starting out don't know the rules of chess?
Here in the UK I have had to call a referee over during a tournament because my opponent didn't know about en passant. And it turned out said referee didn't know either (fortunately the other players backed me up).
Ko variations and scoring rules are kind of inelegant in Go as well. Having to determine life and death under certain scoring systems can be painful for beginners.
I agree slightly about Ko (although it does not seem that inelegant to say that you cannot repeat a board position). However, this scoring complications are entirely a result of players being lazy, the game would be equivalent if you played until the person whose turn it is had no legal moves.
This ruleset would be prohibitivly tedious, but (in Japanese scoring) if you play with the rule that passing requires you to give your opponent an extra captured stone, then the game become equivalent to one where players were required to capture all the stones they thought were dead.
This is even simpler under Chinese scoring, where you would not even have to give your opponent pass stones.
However, because players are lazy, their is no reason to waste time killing dead stones.
Having said that, I can think of 2 inelegences that you did not mention:
Komi, where we give White extra points just because Black was winning to often.