The sheer volume is one thing, but... IAM's policy engine, that's another thing. Up to 5000 different roles per account, dozens of policies that can have an effect on any given user entity and on top of that you can also create IAM policies that blanket affect all entities (or only a filtered subset) in an account, and each policy definition can be what, 10 kB or so, in size. Filters can include multiple wildcards everywhere so you can't go for a fast-path in an in-memory index, and they can run variables with on-demand evaluation as well.

And all of that is reachable not on an account-specific endpoint that could get sharded from a shared instance should the load of one account become too expensive, no, it's a global (and region-shared) endpoint. And if that weren't enough, all calls are shipped off to CloudTrail's event log, always, with full context cues to have an audit and debug trail.

To achieve all that in a service quality that allows for less than 10 seconds worth of time before a change in an IAM policy becomes effective and milliseconds of call time is nothing short of amazing.