Simple idea to balance the game for Black

Black’s long castle places the king on B8 instead of C8.

If the chess community would prefer it, you could also give Black the option of where to place his king when long castling – on B8 or C8.

I think by giving Black this additional option, which allows him/her to be more flexible and long castle more safely, would be a nice and easy way to balance for White getting the first move. 

What do you all think?

Chess is balanced as it is. At top level they get closer to all draws. There have been ideas to unbalance the game to get more decisive results, like stalemate = win, or no castling. To no avail: chess is still a draw even with those changes.
https://arxiv.org/pdf/2009.04374.pdf 

Very interesting and creative idea. It would be great if they could run Stockfish vs. Leela with your proposed change and see what happens. 

The trouble with introducing new rules like this is it negates all the theory for the last 100+ years. There is no problem introducing it as a variant if enough folk are interested, but not for the main game.

ps. In all tournaments each player has the same number of games as Black as he does as White against each opponent. There is no need to "balance" the game.

It's an interesting idea for a chess variant. Would it lead to black castling long more often than short? It would probably need millions of games to understand whether that extra option give black an overall advantage.

How about that plus when castling short black has the option of putting the rook on e8 or f8.

I like your idea. Castling either way essentially would then give Black its tempo back. When grandmasters start with the Black pieces, their goal usually is to play for a draw, whereas with white it's to play for a win. I think the game would be even better than it is now if black also had the same mindset as white -- play to win -- and minimizing the .4 something disadvantage black starts with would certainly help.

#7
"When grandmasters start with the Black pieces, their goal usually is to play for a draw, whereas with white it's to play for a win."
That is not true. Grandmasters play to win against weaker players regardless of color.
Grandmasters play to not lose as white against equal or stronger grandmasters. 
Look at the last classical world championship match: Carlsen won 2 games with white and 2 games with black.

No Castling has already been tried.  Also other types of castling, like the knight move for the king.

The Queen got her current function in 1475, castling became what castling is known as today in 1620 in France and 1640 in England.