The ability of having an API gateway with multiple options like Lambda functions, Kinesis Firehose or SQS is very helpful in terms of flexibility when it comes to integrating different services together.
I'm not sure how easy this would be if you're using other cloud providers but AWS has been great so far! As long as your service meets certain requirements (e.g., lambda function), then everything seems fine. We are solving issues around real-time integrations between our applications that we built internally. This allows us to have more control over what's happening within those apps rather than rely solely on third party APIs which could slow down performance at times.