Of course being able to maintain a comfortable silence with someone is important. But if you find yourself unable to think of things to say to each other, how can you even begin a relationship? Verbal communication and interesting conversations are more important to some people than others. They are extremely important to me. In fact, when you say "friendship works through speech, but I don't think other relationships can," I don't quite understand. Speech (and the written word) is how we communicate. Without the wonderfully complex communication possible through human speech and writing, we would be monkeys. Even my cats understand the words I say (some at least). Obviously, we can pick up other things from people when we're in the same room with them -- or we think we can.
People are attracted to different things. There are people in the world who look for a very physically attractive mate, and that is it. (An extreme example, of course.) However, people who are primarily attracted by intelligence, ideals, common interests, sense of humor, and other mental qualities, are more likely to find a happy relationship on the internet than others. Personally, I could not handle a partner who had completely different interests than me and who didn't share my most important ideals. (I know this because I tried it, and it was horrible.) Others can, and enjoy those differences. I would never claim that their relationships couldn't possibly work just because I know that type of relationship could not work for me.
So, basically, relationships started and maintained (for a time) on the internet can work very well for the right people, and be disastrous for the wrong people. You can remove "the internet" from that sentence and it still works.