Both the analogies you are drawing here are on different tracks - comparing apples with oranges.
You mentioned about a cab driver using a PUBLIC road in his own style. Its on a public field open for everyone, not on a private land.
You also mentioned about American inventions. Nobody is denying that those things are gamechangers, but they were imported and continue to be part of life. America charges for everything - try getting a patented drug from the US. Secondly, America is not complaining that India has made more money from those things. In case of SGX, it is making more money than NSE which is the real issue.
To draw parallels:
A better comparison to make is your parking space, or your lawn. If your neighbor starts parking his car (fully/partially) in your parking space, or in your lawn, that will deprive you of your benefit that you are entitled to (like parking your own car in your own space).
Secondly, say he pays you a small rent for legally using your parking space/lawn, but then starts collecting more rent from other players by sub-letting to park other cars. You will be at a loss in both the cases.
That is what is happening with SGX Nifty. Despite the SGX paying a paltry licensing fee to NSE, they are making more money by attracting more market activity. (similar to case 2 above). That’s why you need to protect your turf.