Preface: I understand how calorie counting can be damaging. I understand how bad it is for people, how much it can mess with your head - I understand how inaccurate and flawed it is, and I understand that different bodies metabolize different ways, meaning calories affect different people differently. I also understand that calories from carbs, fat, and protein are very different from each other in how they are metabolized and what they become.
All that said... using My Fitness Pal and weighing myself daily has been really good for me. Can't speak to how it works for others, but it works amazingly for me.
The reasons for this are as follows.
1) Using that app means that "calorie counting" does not involve obsessing over food, because it's so easy to enter food - and because I don't actually care enough to put in a super accurate number (entirely because of the caveats above). Usually I'll look up a dish on the app, scan the first 10-20 results, and choose the one with the closest to average calorie count, and will only spend time on entering the recipe myself if there's too wide a range of calorie counts to find the median.
2) With numerical backing and overwhelming amounts of data support, I now understand
a. the ebb and flow of my weight from day to day and week to week,
b. how food affects my energy,
c. how exercise affects my energy,
d. how my monthly cycle affects my weight,
e. how exercise affects my weight,
f. &c.
This has helped me eliminate a lot of misconceptions about food, calories, weight, &c, and has helped me remove irrational feelings and stigma from health data analysis. (Basically a Te-user's dream.) Not only that, but it has helped me associate meals with exercise with weight with mood - giving me a better grasp of what gives me energy, what takes away energy, and how that looks in the long term.
3) I have a tendency to undereat under stress, and then allow that undereating to affect my psyche in compulsive and damaging ways. Having a daily structure in which I determine my food based on how I feel physically and how I have been known to feel physically has been amazing for self-care. Thought processes like "You like exercise, and exercise will be impossible unless you have energy, and you need to eat X and Y in order to do that" become much easier when that structure is in place. (Having workout buddies who force you out of the house is helpful for that too, but I digress.)
An example of the above: I realized the other day that, even taking into account my usual weight ebbs and flows, I gained a few pounds. I've been at my daily net calorie marker (give or take a few hundred calories) for the past few weeks. All my clothes still fit the same way, with the exception of one shirt, which fits better in the waist and is now too tight in the shoulders, arms (forearms included), and upper back. I'm physically stronger, and have been doing more easy V2s and difficult V1s at the climbing gym than I ever have. Meaning: I'm gaining muscle. Which I have no problem with. I don't feel bad about gaining weight because my goal was becoming stronger, and I know that this is a sign of progress. None of this would have been possible if I hadn't been tracking my nutrition and exercise.
When I started using My Fitness Pal, it was an experiment to see if I could track my calories and learn about how I eat without spiraling into body image problems and disordered eating. The result is that I've never felt better about my diet and exercise. Not because I've been eating better or exercising more - even though (for the most part) I have been. It's entirely self-perception. I don't stress about food or exercise to the degree that I used to, and as a result I feel better about myself.
Per the preface, I'm not evangelizing this, and I wouldn't recommend this to most people. If you've got obsessive tendencies, self-destructive tendencies, or body image issues, handle with care or avoid altogether. But I've come away from this feeling pretty amazing.