SOME five hundred years ago there lived this renaissance guy, bent on looking at things in a new light, as was the fashion, and being a Shatranj player, he looked a lot at Shatranj. Suddenly it hit him: the bishops were crippled.
We agree, they weren't even bishops. They were "fils". They could jump diagonally to the second square, leaping the intervening one. They had only seven squares in total. They could never attack one another. Our hero suddenly realized they were pathetic.
And so was the "firzan" or minister, that had a one square diagonal move and was the only piece a pawn could promote to.
There were a couple of additional rules that we would consider rather odd nowadays - they don't matter here. What matters is that our hero came to the conclusion, obviously, that the whole concept needed rethinking.
So he did: he liberated the fils and made them bishops, and gave pawns the right to promote to any piece.
In this environment the firzan of course became even more pathetic, and here he made the boldest step (therewith implying Grand Chess in the concept).

Combining powers
He combined the powers of bishop and rook and turned it into a piece of unprecedented strength: the Queen.
This was a very bold step indeed. We look upon the queen as well within the boundaries of balance, but 500 years ago its power must have seemed unbridled.
He may well have been aware of the rook-knight and bishop-knight combinations, but straight and diagonal are clearly the first movement options to be considered, so the choice that the 8x8 board forced him to make was logical.

Rook development
Rook development constituted a problem. The problem with rooks is that they are obstructed by their own pawns, unlike bishops and knights. And precisely the rooks were tucked farthest away. Maybe our unknown hero didn't think of it, but someone did, and came up with castling.
Castling serves rook development as well as king's safety, but the latter can hardly have constituted the argument for it, in a Chess game.
We're so used to castling that we tend to forget that it is the weirdest move in Chess, implemented specifically to solve a problem. Chess turned out a great game despite its problem, but it needed an ad hoc fix to do so.