This answer is a more "what value does an API Gateway provider bring" than Kong specific as it's been a couple of years since I did an in-depth comparison of the different options.

Say you have some developed kind of consumable service (think like fraud detection, geolocation, or machine learning recommendations, whatever) then using Kong or another API Gateway as a service type offering is a way to handle big chunks of all the boring but necessary infrastructure needed to bring that to market.

This is stuff like setting up plans, accepting payments, rate limiting, issuing and revoking api keys, docs, etc.

API Gateway's function like a proxy or CDN where api.example.com goes to blah.kong-api-service.com which then requests back to your-app-server.example.com so they're able to do these things without needing to get into your code.