The whole point of exponential backoff is that the first retry can be quick.
When one end user request fans out to hundreds of backend requests (typical for microservices), you can't have each of those backend requests do its own exponential backoff. If they do it in parallel, they're a thundering herd, and if they do it in serial, the end user request will time out before you finish all the work, at which point you're doing a bunch of slow expensive work for no gain (and the enqueued slow expensive work will make your outage worse).
There are client-side retries (which have broken GitHub in this case) and server-side initiated API calls between microservices that don't pass through any of your ingresses (e.g. triggered by an ETL pipeline, or a scheduled job).
With a complex architecture you can't just slap a circuit breaker on a couple of ingresses and call it a day. Don't get me wrong, putting them there does go a long way, but you won't be covering all your bases.
At least it should be required for critical level services in production.
“Circuit breakers, where calls to a downstream service are stopped entirely when an error threshold is exceeded, are widely promoted to solve this problem. Unfortunately, circuit breakers introduce modal behavior into systems that can be difficult to test, and can introduce significant additional time to recovery. We have found that we can mitigate this risk by limiting retries locally using a token bucket. This allows all calls to retry as long as there are tokens, and then retry at a fixed rate when the tokens are exhausted.”
I’m particularly fond of the token-bucket mechanism for pacing recovery.