If you run it behind CloudFront it does support HTTPS.
My personal website is low-traffic, it’s not going to be very hot in any CDN caches. Based on my experiences with S3 performance, adding another layer of cache misses in front of it is probably just going to slow things down.
The suggestion was more for the HTTPS part and not the performance part of your complaint. It's simple enough to set up, pay-as-you-go, only requires one vendor, and should be very scalable.
I'd just as soon throw up nginx on a Linode, myself.