Why is the total amount of bitcoins that can be mined just 21 million?
The answer would be funny. The number of 21 millions could be chosen “randomly”.
Back in 2008, when Satoshi designed Bitcoin, subjected to the internet speed at that time, 10 mins (roughly) per block was chosen to avoid frequently hard forking. And 50 BTC per block sounds like a nice number, and then halves every 4 years thereafter.
So the limit of Sigma (Block Rewards_i X 6 X 24 X 365 X 4) is almost 21 million
Block Rewards_i = 50 / 25 / 12.5 / 6.75 ….. / almost 0