Yes and no. To get a little bit meta on you, isn't it true that just as different people need different amounts of sleep, different people also have different needs in terms of active monitoring of their sleep? Some, like you, are better off just trying to relax and not stress about the time they spend sleeping, but others actually do benefit from the certainty that comes from an accurate measurement. It kind of feels like you're trying to advocate your own one-size-fits-all solution ("Just relax and sleep when you're tired") while at the same time objecting to another one ("sleep 8 hours a day").
I think there's a decent parallel to the notion of dieting, where I too take a view roughly equivalent to yours - simply eat when you're hungry, and stop eating when you are no longer hungry (but before you're completely full). Trust your body to know how much it needs. For me, obsessively counting calories would be torture, and I have a vague belief that a lot of eating disorders are caused by over-obsession with calorie counts; but at the same time I recognise that for a lot of people, my approach simply would not work, and tools that help people stick to their diets are, on balance, a good thing in the world. And so it is with sleep monitoring apps - which are useful, if nothing else, for reminding you of when the right time to go to bed is.