Would a site without a particular niche work?

I have an idea of creating a site where I post about EVERYTHING! So, the relevancy score would be non-excistent between posts but if the domain gets a nice PR and DA/PA then it would still benefit each post. What do you think of this idea, could it work or would G just decide that the site is not "authority" in anything and therefore the kw-s would not rank that well (even the low comp ones)?

Just because a site doesn't belong to a specific niche that doesn't mean it can't be an authority site. Go for it.