I don't get it - it is a nice sentiment, but the crux of the argument seems to "go with your gut." The reason web analytics has been so popular is that you can actually improve your product significantly without as much subjectivity. Before web analytics, going with your gut was the only option. It turns out, threading events through a funnel that show you lost 90% of your users because your button doesn't show up on certain screen sizes is a meaningful capability. The question from there is how far do you go with it, but I don't think it makes any sense to both reject it and go on to propose such a fuzzy, underdefined alternative as "you'll gain intuition about if you're making connections."
Having built a number of apps, I don't know how to gain such intution once the userbase becomes too large to interact with directly enough to grok it. It's very easy to be fooled by a vocal minority of people who complain about your app sucking when the majority are getting value from it. Without data and analytics, it's easy to be pushed around by your most vocal users, because your gut is saying you should listen to them. Sometimes you should, sometimes you shouldn't, but the difference between the two can often be determined by looking at the data to get a bigger, less biased picture of what is actually going on with your app.