We're completely noob in this automated bot publishing space, so please bear with us :)
We have observed that to make a Messenger chat bot publicly available, we need to get it manually reviewed and only then it's available to the world.
However, chatbot builders like chat fuel & motion.ai do AUTOMATICALLY publish the bots without any manual review process.
A brief guidance so that we understand how these provider are providing automated bot publish will be much appreciated.
You don't review the chatbot manually from Facebook.
However, You must need to submit the Facebook app for manual review which serves the webhook to your chatbot (all chatbot associated with that app, to be precise).
As you mentioned chatbot builders like chat fuel & motion.ai do AUTOMATICALLY publish the bots without any manual review process.
They allow chatbot publishing using platform which in backend uses the FB graph API's to link the chatbot to there app, the app which they have already reviewed from FB. In layman term, single FB app serves to multiple chatbots.
Are there any APIs which does automatic bot publishing? Yes, FB graph API is the answer for it. Search for Webhook API.
How is the App review process automated? No, App review process is handled by FB team itself.
OR, is the app review process completely omitted? No, You can't omit the app review process.
So technically speaking, there is no way around to avoid the app manual review process. This is the one-time process. Once your app gets reviewed, you can allow any chatbot to publish in association with your reviewed app.