$1.20 a month may be expensive relative to your costs, but relative to the average programmer income and monthly bills in the United States – it's nothing. You'll spend three times that cost on a local cup of coffee every morning.
S3 static hosting is far easier to manage than a virtual server; it's a trade-off of convenience vs savings.
I've used digital ocean droplets for some things for a similar $5 a month price, but it hardly seems necessary for a static site. It's much less faffery to just upload some files to S3 and click some buttons in the AWS console to configure everything.
I'm really conscious about the resource usage of my server processes. Most sites are static websites, but I also have Gitea, Prosody and Matrix Synapse running on that box, plus some small Go webapps for my own consumption.
EDIT: I just realized that's a question I should ask: Does your price include the domain?