I don’t think they should be considered silent letters. They are usually used in combination with other letters, and change the meaning or sound of that other letter. This happens in many languages. Hebrew, for example, has a whole set of diacritical marks that represent vowels. If I understood it correctly, they don’t have any characters for vowels, just these marks that tell you how to pronounce the consonants. This may have been an older system which is now being replaced by a system that includes vowels. Someone should correct me if I’ve got it wrong.
In spoken language, you can hear the differences in pronunciation that give you clues as to meaning. Written language doesn’t have sound, so it depends on visual clues. In English, we use letters that have other uses to modify other letters. It’s more efficient that way. We could have additional characters that serve as modifiers, but then our alphabet would expand and become more unwieldy.
I think there are silent letters that don’t serve a pronunciation purpose any more. However, they do serve to enhance meaning, because they are clues as to the derivation of the word. “Debt,” for example seems like it should be a shortened version of “debit.” “Pneumonia” is based on pneuma, or breath—a Greek root that, if you know it, can help you with any number of other words (pneumatic, pneumococcus).
In Greek, genomos means earth-dweller. Thus gnome tells us something about its roots. The kn cluster comes from Old English, where it was pronounced. It has not yet been removed as some other silent letters have, and as @gemiwing said, it is a visual clue that we are dealing with different words. Although we deal with a few other words that are spelled the same but mean different things just fine.