TLS ensures that stream was not altered. Any further checksums are redundant.
This is actually not the case. The TLS stream ensures that the packets transferred between your machine and S3 are not corrupted, but that doesn't protect against bit-flips which could (though, obviously, shouldn't) occur from within S3 itself. The benefit of an end-to-end checksum like this is that the S3 system can store it directly next to the data, validate it when it reads the data back (making sure that nothing has changed since your original PutObject), and then give it back to you on request (so that you can also validate it in your client). It's the only way for your client to have bullet-proof certainty of integrity the entire time that the data is in the system.
Anybody have sizable examples? Everything I can think of results in dedicated gpus.