Thanks, I am aware that you can inspect the network request and use that URL to make a form submit request, like you did in one of the posts above https://github.com/Coding-Enthusiast/SharpPusher/blob/master/SharpPusher/Services/PushServices/BlockDozer.cs
But I think calling that an API is same as calling all HTML forms on the web an "API". You can theoretically take any form on the web, take their URLs and emulate submit, and call that an API. But you wouldn't be able to rely on it since they can always block you from using that approach.
None of the sites mentioned on this thread as far as I have looked into has an actual public API endpoint, which was what I was asking for. Services like Infura or MyEtherWallet have an official "API" page that makes it public that they want people to use their node as a broadcast service.
The problem with emulating form submits from the sites mentioned on this thread is you can't really rely on them because they never said it's OK to use their form as your API. If you rely on them to build something, you can never be sure that one of them will just block you one day.
I was looking for a service that explicitly provides a public API for bitcoin transaction broadcast, and it would be interesting if there isn't one. (My followup question would be, why doesn't it exist, unlike Ethereum?) Or maybe I'm misinterpreting this and actually all of those sites--which seem to be powered by the same open source project--DO provide the API implicitly by default?