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.
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.