My mentor always taught "Program as if it has to run on the far side of Mars."
Software that doesn't need the internet for its function shouldn't connect to the internet. Software that does need the internet should be able to operate under adverse network conditions.
The Voyager probes are 160 AU away, far past Pluto, with a roundtrip latency of 37 hours. The radio transmitter onboard is only about 10x more powerful than a cell phone. The hardware has been in the cold vacuum and hard radiation of space for four and half decades. In spite of this, NASA maintains active two-way communication with it today, and continues to receive scientific telemety data of the outer solar system.
I don't expect web devs to design for deep space, but the core functionality of a website should still work for a rural user with a spotty satellite uplink. Don't do go loading JavaScript or other resource calls until the basics are received. I still remember the days of Facebook being fully functional on a 2G cellular connection, using little or nothing more than static HTML and CSS (and that was before the magic tricks HTML5 can do).