It's not that "less text is better", actually, depending on your page and what you're trying to sell more text is often better. If you can write a long, engaging sales pitch it's much more likely to convert users than a short one, because those that read it all have will have already invested time and effort in your site or product and want to get something out of that investment. The key is in finding the right balance - don't overwhelm the user with a giant wall of text, give the already "pre-sold", impatient users an easy way to convert and let the more cautious users keep reading and scrolling down. Typography plays it's part in establishing the content hierarchy, but to say it's the most important part of the design is pretty silly - it's one of many important parts. The actual physical arrangement of page elements is far more critical. (Of course, awful typography can ruin a site, but so can many many other factors)
Design, form and function compete for limited space and try to advance towards that goal by picking the perfect mix between conflicting goals. It should look good, it should work and what text you've got should be readable.
But not all websites center around the written word, and user experience is not just reading text on a website.
Hint: Less text is better. So good Web Design is to avoid having the problem that 95% of your web design centers around typography or any other single metric.
It's the total package that matters and typography is but one (minor) element in there. If it isn't just the right font but it is readable you're already 90% there, the remaining 5% may or may not be important to you.
I know great sites that use 'courier' or some other minimalist approach and I know sites that suck that have been designed by the best in the industry, they look great but they're like super nice wrapping on a shitty present.
Strike the right balance, don't worry too much about any one factor, especially not typography. After all, the screens we have are direct descendants from the 8x6 dot matrix fonts of not that long ago, the availability of information is what drove this industry, not the availability of high resolution display for typographical purposes.
We don't call them graphics displays for nothing, pictures still paint a thousand words.