I've been running https://jsonip.com for years. Been serving millions of requests a day for most of that time. Doesn't really show up in searches well because it's just an API.
I run a few small services, nothing of this scale, but one thing to bear in mind is that it's easy to pay for a lot of little side projects if they have virtually no costs.
The one cited simply echoes back your IP. That's it. How cheaply could you do that and how many requests per second could you handle on one small VPS?
Example, I recently ran https://www.tactical2017.com/ which is a tactical voting website for the UK general election. The cost for serving that whole website to 2.6 million people over 5 weeks, and 650k people in the last day and a half, was $20.
I use linode. Been a loyal customer from years. Basic service is $40 a month with $10 for automated backups. Fits within the bandwidth contraints. I've also spent a lot of time optimizing the hell out of the server.