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In fact, the trumpet with its approx 5" bell is very directional for the highest overtones.
Loudness is a perceived unit of measure and it is very difficult to objectively define it. Fletcher/Munson is a good start and may even help here-more on that later.
When we try to play above a certain pressure (different for each horn and player), the fundamental tones become masked by distorted overtones, increasing the pressure does not increase acoustic output, but changes the relation and nature of the overtones to the fundamental tone being produced. This effect can be observed with any measurement of distortion in audio horn loudspeakers. At a particular output level, distortion increases very rapidly. This is not just a function of the horn, but also the interaction of the horn and the driver(or our lips). The reflections in the horn change the pressure that the driver or lips "see" and this pressure is not linear throughout the frequency range.
To keep this simple, playing in the optimum pressure range that our lips/mouthpiece/trumpet can handle, gives us the most resonant sound. If our embouchure is not strong enough to support the pressures developed in the instrument, the lip movement becomes distorted and the effect multiplies.
Distortion increases the high frequency output and if we look at the Fletcher/Munson curves, our ears are less sensitive to high frequencies - we think that we are not playing as loudly. Once that "distortion level" has been reached, the lips are no longer in control and the tone quality suffers. The best players have the best "control" of the driver (the lips) and can keep the distortion acceptably low at even greater pressures.

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