Not only should developers design for slow internet, they should design for no internet. Shockingly, many parts of the US don't have solid cell phone coverage. Even more cell phone towers have broken uplinks or broken configurations; your phone connects to the cell, but no data flows. Cells get overloaded - at fun things like sports events and concerts. They also get overloaded at very not-fun events like natural disasters where everyone is standing around the (very overloaded) Cell On Wheels tower, trying to get a message out to their loved ones that they're OK or need help, or trying to reach their insurance company, or access a government website to get info about disaster relief, etc.
It's infuriating how many smartphone apps will show you a screen full of the information you need while online, and then when they lose internet connectivity due to a dead spot in cell coverage, yank it away leaving you staring at a blank screen with a spinning progress indicator.
It's also infuriating how so many apps are completely, totally non-functional if they don't have internet, if only because they're not actually a native smartphone app, but a website being run in gussied up web browser instance.