Yep. They are an important indicator of how to pronounce a word. I thought the same thing was true in English, but now I’m not sure..

Generally the "rule" in English is the same as the one in German: a double consonant ensure the preceding vowel is pronounced the short way rather than the long way.

The saddest sadist, the matter of maters, and the bitter biter, for example.

That’s not long or short, but different vowels entirely. A better spelling system would express the diphthongs explicitly, or at least as diacritics.

There are soo many different English accents both within the UK and around the world that consistent pronunciation isn’t guaranteed.

Tomato, Aluminium, Chips, Craig to name a few off the top of my head.

How is Chips pronounced differently?

I've heard that it's common to use the phrase "fish and chips" to distinguish between Australians and New Zealanders.

Had no idea, but I found an example now, thank you!

For anyone else who wants to hear this difference:

https://m.youtube.com/watch?v=XKuPfZpzEHg

It almost appears as if they were referring to the American alternatives, Aluminum and fries.

I'd have thought the accents argument would apply to any location, Germany included.

German dialects are rarely written and if they are they are written different from Standard German. The written German language is very phonetic and if you know the rules you know exactly how a word is supposed to be pronounced.