Making the "check website" free (forever) should be pretty simple, but that's really only a part of what's valuable. Things that could be add-ons to encourage a subscription once verified that the service is simple, works, and saves time:
* Additional subdomain checks.
* Deep page checks: JS, CSS, images, everything beyond the initial HTML and "yes, I received an OK 200". Make sure the whole page loads.
* Test that intra-site links on the page (e.g. page "/a.html" links to "/b.html") work.
* Report any JS errors on page loads. Also and console.log output and "debug" things like map files, Vue.js/React tools that shouldn't be enabled in production, etc.
* Test with different User-Agents to follow any redirects (e.g. to mobile subdomains) to ensure the site is doing the right thing.
* Use libraries to fully load the page(s) using different browsers and devices, capture them, and show thumbnails/screenshots of the page fully rendered across browsers and devices.
* Provide a REST API so that as part of a CI process someone can call it and have their dev site tested.
* Test REST APIs, logins, analytics, etc. for sites where users can create specific tests that run. Also test correct response codes for expected failures (e.g. access denied).
Anyway, there's likely other services that do similar things. I'm not experienced enough in this area to know all of them, but the above are things that I wish were easier for me - and my team - to test regularly.
Hope some of this helps.