Calculate the overall averaged 4pi level, compare it to on-axis per frequency-band, you get the d.i.. In the old days this was done with one measurement under anechoic conditions and the other one in a reverberation chamber.
As mentioned, it is not perfect, and bandwidth-limited due to cabinet size and choice of tweeter, but more or less balanced. There is no 1/3-octave band between 700Hz and 6,000Hz overly deviating from a +-1dB tolerance band in d.i.
I have been dealing with polar plots and resulting d.i. calculations comparing them with listening tests on a professional level. I know how to read the graph, and I know how it sounds in different rooms.
You might be visually focussing on the -3dB or -6dB isobaric line or its change in color. This tells you something about the attenuation at a given frequency or angle when leaving the optimum listening window, but the overall averaged energy in the room is a different thing. Look at the calculated d.i. over frequency which is a much better indication.
What you call a ´widening´ is like +1dB in indirect sound level. Would argue that it is barely audible under usual conditions in a smaller room, in a frequency range which usually is seeing a mild decrease in RT60 due to increasing absorption grade of materials.
But we agree on the problematic behavior of the tweeter beyond 8K. Toe-in might bring some more upper treble but usually comes at the price of less precise or less stable imaging. It is a common thing with these ring-radiator type of tweeter.
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