...Can we now ask a more advanced question of why the 21 million choice. Any mathematical arrangement supporting that? I mean why not 20 million BTC which is even a round number than 21 million.
Here it would be more correct to ask why Satoshi chose 50 BTC as the reward for the first block and the fact that every 210,000 blocks, the reward is reduced by 2 times, since this is what affected the total issue of bitcoin in the amount of 21 million. Thus, before the first halving, 10,500,000 BTC were mined, respectively, by the second halving, 2 times less BTC was mined - 5,250,000 and so on. And you don't have to check that the amount of all BTC mined by the last halving will be exactly 21 million.
So the question remains, why was the reward for the first block chosen by Satoshi in the amount of 50 BTC and why were 210,000 blocks chosen before the next halving?