Although the idea is simple, this need is typically satisfied by a free uptime monitor for me. If I need it to stay up, I might as well let somebody monitor for downtime and alert me.
In what use case would you prefer your solution over an uptime monitor? like e.g. https://uptimerobot.com/
Why would one want their Heroku instance to stay awake at all times? If the request is processed with a slight bit of latency, I'm okay with that. Plus, it helps the Heroku guys manage their infrastructure and cut costs in terms of unused computation time. This feels like taking advantage of the good will of those providing the service.
the first time the instance can be very slow. Like 20s response time.
Are you sure this isn't against Heroku's TOS?
the more common way to do this is with new relic's uptime monitoring. I don't think heroku cares.
My assumption is if you're at a stage of dev worth running New Relic then your app is probably worth the constant uptime. Out of the dozen or so Heroku apps I have only one or two are using New Relic. The rest are just experiments not worth the additional infrastructure waste.