If you're running on AWS it's really nice to have everything preconfigured for things like logging to Cloudwatch, and not having to mess around with kernel optimisations.
Ubuntu considers AWS/GCP to be certified platforms so the server is fully tested on AWS as a hardware platform and there are specific kernel/toolchain/user-space optimisations done to make it run well [0].
The advantage of one of the existing distributions over Amazon Linux is that they are available and tested across multiple clouds, hardware platforms and range of software.
In theory, since the kernel is specifically tuned towards running on EC2 virtual machines (by the people who know EC2 virtual machines better than anyone) as opposed to 'generic' hardware, performance might be slightly better.
Also, and for many more importantly, it's probably easier to get support from Amazon if you're using their official Linux as opposed to a third party distribution.
Your first point is not true compared to Ubuntu at least [0]. AWS is basically are repackaged version of KVM (the last time I checked), so there's no particular advantage. Ubuntu (and I'm sure Centos/RHEL) provide custom images which have the same optimised code.
[0] I'm pretty sure it's true for CentOS / RHEL, I just don't know for a fact.
AWS is mostly Xen (they just introduced a KVM option https://aws.amazon.com/blogs/aws/now-available-compute-inten... ), and there are a few things like "enhanced networking" where you get a performance boost if you're on a kernel with support but it's still functional if you're on any other kernel.