> I don't care. The site is doing something unusual. It's evident, it's enough to take a second look and think about it.
Is it enough to do an informed decision?
> Again, as a layman, I don't care.
You do care, whether you mistyped or the network is down. I agree that you probably don't care to distinguish between "network unreachable" and "no route to host" though.
> As a sysadmin
True, but that information was already there and was thrown away.
> Is it enough to do an informed decision?
With my layman hat, yes it is. I'll think about a trade-off between site's importance in my life, trustworthiness of the body behind the site, and my privacy.
> You do care, whether you mistyped or the network is down.
No I don't. Because it's easy to check for a typo, and then it's easy enough to investigate like layman. e.g.: Try going to Google, check for your (wireless) connection from your taskbar, every OS shows a "!" when internet is unreachable, and so on...
> but that information was already there and was thrown away.
Sometimes starting with a truncated but accurate info allows a way faster start. Precision and accuracy are different things, and accuracy is more important than precision.