Surely if you're building microservices, this line of thinking would be a failure to stick to the design? If your failures aren't isolated and your APIs aren't well-made, you're just building a monolith with request glue instead of code glue.
I appreciate the point is more that this methodology is difficult to follow through on, but integration tests are a holdover - you can test at endpoints: you should be testing at endpoints! That's the benefit.