I wonder if your point about pen and paper feeling like it worked better is because the app approach puts even more focus on the component data itself and not on what is probably more important - what we actually need do to reach our end goals which is not always so obvious.
A big problem I see with a lot of the current generation of health apps (at least those I have used) is that they've become pretty good at capturing and presenting data (making it pretty) but there's often still a huge gap to fill on actually interpreting this data and telling the user what they now need to do to improve and reach their goals. That's where I personally feel the real value is. (And to be honest I think this is a theme outside of health apps as well...)
Again another personal example - I've been getting into running more and more over the past few years and like a lot of people have been using GPS running apps to track the runs (Runkeeper, Endomodo, Strava etc.). The majority of these apps gamify and give encouragement on things like fastest mile/5k/10k, average pace for the month, frequency, longest distance etc. So as an unknowledgable and fairly ignorant runner I've ended up just trying to beat these metrics - by trying to push harder and run faster on every run.
The problem is it's only recently, now that I've become more keen and have started doing research, that I found out that this is completely the wrong way to do things. Almost any decent training program or coach would recommend running at different paces on different runs and spending up to 70-80% of your training at a relatively comfortable, easy pace [1]. This is much more effective at helping you to run longer, faster and avoid injury.
And it's this knowledge that was completely missing from these apps.
PS @tomeglenn, I love the idea of the app "measuring what really matters" - and in a way addressing the problem with BMI. If you can make the measurement as easy as possible that would certainly be a bonus. But for me combining it with coaching/education on how to actually reach goals (rather than just setting the goal and tracking/rewarding the deltas along the way) takes it to the next level, although is probably much harder to do. Best of luck, and congrats on shipping!
[1] http://www.goodrunguide.co.uk/TrainingGuide.asp