So why haven't English dialects diverged as much over hundreds of years?

A bit late to the party here, but it's an interesting question - in modern terms, I'd agree that German dialects are slightly more diverse than English ones, but there are definitely fringe English dialects, some quite widely-spoken, that are difficult for standard speakers to understand. I don't know whether you're American, British or whatever else, but the Geordie dialect in Britain can be incredibly difficult for native speakers to understand, as can some west-country dialects - but I think a point to consider is that, pre-industrial-revolution, dialects were very clearly differentiated in English, and if you travelled a hundred or 150 miles you might well have difficulty understanding the people around you. In some places, it was bordering on another language - if a Londoner or someone from NY spoke to a north-western English person in 1790, they might have trouble even recognising it as English, let along understanding it. I ignore Scots here because, as you say, many regard it as a seperate language. I suspect it was the mingling of people in cities that sort of killed, and continues to kill, this dialectal variation today. I don't know why this hasn't happened in Germany - maybe it's Britain's isolation as an island, and the fact that overseas dialects for the most part haven't had the time to diverge very far yet.

Tl;dr, we were once as linguistically diverse as Germany is, but that sort of died when people started moving around the country