Good idea! The system can even have a message that says, "Although we plan to open at 9am, nobody has arrived to turn me on yet."

It could have to deal with scarcity, as time that is scarce is perceived to be higher valued, as booking office hours with a professor, for example. But that's just my economics take on it.

Regardless of that, it still makes no sense to time-constrict a websites uptime. It's not as if websites run on manual labour! (well, it takes some to create one)

The irony is that a site that says "someone needs to come in and turn me on" must already be turned on. They've already written an app that has 100% uptime, they just use their uptime to claim the system is down.