If it's only a cache it should be on EBS, which is still way faster and 2x less expensive.
I started a migration to s3 for such a project (container image caching) but then stopped when I realized what I was doing.
[1] Yes, I am aware of multi-attach but this introduces a scaling bottleneck and requires a fairly exotic setup.
2. Variable throughput may be a concern.
3. You may have availability concerns.