The downward-sloping distribution of frequencies across the audible spectrum typical in the vast majority of recorded music shows a significant drop in the range reproduced by the tweeter relative to the bass frequencies (see links below). Historically, the 60-80Hz region has been on a red-hot melt-up during the past few decades, with the advent of electronics and hip-hop/rap music.I doubt a 1 watt signal would fry the tweeter
Using an xover and could you be more specific about JA measurements , what about it is incomplete or sub optimal ..?
Try playing a demo/test disc containing warble tones, and the half-octave centered around ~4kHz (where the ear is most sensitive to) is painful to listen to even at 85dB, not to mention 88dB (double the power), or god forbid 91dB (quadruple the power). Even assuming that the typical loudspeaker has a low acoustic tweeter output sensitivity at the listening position of 85dB/1W, it will only require 4W of power to produce 91dB (assuming power linearity).
The typical delta of -24dB between 200Hz and 4kHz (limiting the range to be music-genre neutral) implies a power factor difference of 2^8, or 1/256. Normalizing the tweeter reproducing 4kHz with 1 watt of power, that’s 256W into the woofer (ignoring room boundary reinforcement effects in the bass and absorption/diffusion effects in the treble).
http://eecs.qmul.ac.uk/~josh/documents/2013/Pestana Ma Reiss - AES135.pdf