I haven't come across any website that use monospace fonts as the base font for their websites. Why is that?
Does the website necessarily look bad when you use monospace?
It may look rather obsolete, probably that's why it is avoided, it was used rather heavily in the 90's along with animated GIFs and starred backgrounds and it didn't look very well.
Also it would be confusing since another monospaced:
Courier New is used for preformatted text in
<pre> blocks. So there is almost a convention that monospaced fonts are used for code and preformated text.
But I see no reason why not to use it, if you can find a good looking template, otherwise the above concerns might apply.
I think the answer is simply that most humans will find blocks of monospaced text harder to read than text that is proportionally spaced.