No. BMI is designed for naive people two hundred years ago who just want a number, no matter how meaningless it is.
Weight does not and should not scale with the square of height unless you imagine that taller people are taller and wider, but not thicker. It's not a cubic relation either in reality, but there would have been more logic supporting that than square, even if it's a no better fit to common-sense results wise.
Everything to do with exponent-2 BMI should just be totally ignored. It's total bullshit. It says no more, and plenty less, than a whole range of other measures that aren't bullshit. It should have been thrown into the toxic waste bin of stupid medical superstitions that's of no use to anyone decades ago.
We do some work in the field, in governmental contexts. We've come up with phrase "policy-based evidence-making" for such bogostats.
What's your BMI using a 2.5 exponent, as proposed here?
http://people.maths.ox.ac.uk/trefethen/bmi.html
(And no, sorry, I'm not volunteering mine on either scale, given where on the bell-curve I sit. (yes, the flat bit.))