Is that the reality of owning a website?
For example, if you use Wordpress, you’ll have to keep updating WP because of security risks, but then you’ll also have to keep adapting your templates to keep up with the changes in WP.
However, once you no longer need to update the site and simple want to display its contents, you can fix it in time by crawling the website, in much the same way that the Archive team is doing now. You end up with a collection of HTML files that you can host with ease and minimal maintenance. If you do it properly , you turn off commenting beforehand so you don’t end up with non-functioning links, and you create an .htaccess that makes sure the old dynamic urls get correctly mapped to your new static files.
I’ve done this, it’s not rocket science, it’s not unreasonable to ask this from Amazon, and I wish it was standard practice for sunset websites.