Satoshi wanted BTC to be like gold: initially easy to create but then increasingly more difficult. I don't think he put a ton of thought into it. This algorithm will work fine, though.
It's kind of odd, though, that he would just arbitrarily pick a tapering-off point, after all the work he put into the rest of the system, isn't it? It's almost like he didn't care about the economics of it, and just wanted to test the soundness of the algorithm for handling transactions.
There is no perfect curve. Technically to keep stable value the money supply should grow at the same variable rate as economic activity. That is simply impossible to predict ahead of time. In a centralized currency this is the job of central bank. If you have 5% economic growth and central bank using monetary policy causes a 5% growth in money supply economic theory tells us the value of the currency should be stable. If money supply growth it higher the currency would lose value, if it is lower it will gain value.
Lacking a central bank of bitcoin to manage generation rate any curve will be imperfect.
The curve chosen isn't perfect but it does have some advantages. It rewards early adopters (note that term is relative. You are an early adopter compared to someone who starts in 2018), it results in continually decaying inflation, and it allows Bitcoin some time to gain critical mass and organize a sustainable fee structure before the block subsidies begin to decline.