Say for example, if all your users start spending 30% more time in your reset password page after you pushed out some changes. How would you know? What could be causes of that? Could something be broken with the login? Apply this to everything.
Not having analytics is literally not caring about what they do in your product, so you're either never changing the product and 100% confident it'll always work, or you're probably giving them a worse experience than you could.
How you do this tracking is another story, but there's ethical ways to do it.