iOS made the mistake of conflating wifi with “internet”, it will even attempt to kick you off a wifi if it doesn’t have internet, but it will gladly show you the icon even before logging you into the captive portal.

The current situation is incredibly badly-engineered on so many levels. It’s maddening, really. One of the worst parts is that the modal disappears as soon as you attempt to switch apps (or god forbid you try to respond to a message you received)

Notification + real internet connectivity indicator + a regular Captive Portal/Internet App would go a long way.