Your biggest issues with that setup will be:
1. Credential and permissions management. Don't lose control of your access keys to AWS! Set up "MFA" at the very least. If you use your AWS account for other purposes, use IAM to ensure that other users cannot access the S3 bucket with the site in it.
2. Getting that green lock (e.g. HTTPS). You can pay $800/month or something insane to Cloudfront to get a custom TLS cert on their CDN, or you can get Cloudflare's "universal ssl" for $20.
3. DDoS is not really a concern. It would be nearly impossible to DDoS an HTML-only website hosted in an S3 bucket. I'd really like to see someone try. The only thing that could happen is you get charged a bit more that month while people are DDoS'ing you. But if you're behind a CDN like Cloudfront or Cloudflare (which can cache everything because it's plain HTML), then the impact would be reduced.
4. Your Registrar suddenly becomes a huge risk. Make sure you use a secure domain registrar (ie. NOT GODADDY!), that the registrar has a "Registrar-Lock" turned on for your domain, and that your account with them has 2FA. If you screw that up, then someone might be able to socially engineer the phone rep at the registrar to transfer the domain, change the nameservers, etc. This happens depressingly often.
5. 3rd party services you use could get hacked. You'll likely import a bunch of JavaScript from other websites onto your own. If any of those websites get compromised, it might affect your website too. Make sure to use 2FA on every service you can (https://twofactorauth.org/) and minimize the amount of JavaScript/fonts/css/whatever that you load from 3rd parties (re-host it locally).
I highly recommend setting up websites this way. It's fast, easy to maintain, and incredibly secure. We do this for the trailofbits.com website and we're very happy with it. Jekyll FTW.
ps. don't forget you can use Github Pages too.