AWS offers Cloudfront as an alternative to Cloudflare. Serving traffic straight from your S3 bucket is wrong. S3 stands for Simple Storage Service and they really mean it - it's a low level object storage service intended for programatic usage that does exactly what you tell it without any caching or anything else, not a web hosting. Add Cloudfront and your costs will instantly lower multiple times. AWS tells you this during S3 bucket creation when you try to make it public, btw - it's not hidden.

Cloudflare networking solution doesn't nearly match - and to be fair, they're not trying - what AWS offers. Cloudflare is a small, focused service; AWS is enterprise universal do everything and stay secure&compliant while doing it solution that has the entire Cloudflare offering included and it's not even a big part of AWS. Don't conflate the two - use whatever is better for your use case, budget/margin, risk profile, reliability requirements etc, but each has some and the price is justified.

Are you sure you are AWS partner? Cloudfront is not going to "instantly lower multiple times" - it's still $0.060/GB (for US, other countries are even more expensive), so that would be at least $6K monthly bill. Its only few tens of percents reduction.

And sure, Cloudflare does not have all the breath of Amazon services, but I find it hard to justify $60 vs $6000 price difference. Amazon egress is simply incredibly overpriced, and any price-sensitive company should avoid using it.

It is not overpriced, it's simply not fit for your purpose - that's all I'm saying. That's fine, use the best tool for the job - I use Cloudflare too, it's great. But there are times when the capabilities offered by AWS networking are necessary and the price is well justified for what it offers.