Seems like a waste to pay for a month of VM time when only a few milliseconds are actually used. I like the idea of FaaS where I'm not being charged when my code isn't running.
So by my estimates, even if the small utility is #1 on HN for a whole day, it's not going to cost more than a dollar.
Maybe there are more hidden costs, or maybe the small utility uses a lot of runtime though, so you could be right in the right circumstances.
Taking the statistics from some old Ask HN thread [0] (which is probably an underestimate?) you would need to render your site in less than 2ms to stay below 1$ for that day. And serve less than 51kB of data per page view to stay in the free 1GB of traffic region (this part should be pretty doable if you don't include any large images).
Of course assuming you don't have any existing VM or web hosting you could reuse for that.
Edit: Ups.. Used per-second billing instead of per-ms by accident. So even up to >1s per request it's below 1$ for that actually. So only leaves significant more traffic and lots of bandwidth usage as possible sore points for tiny web services.