Higher frequencies can easily be tamed with basic treble tone control.
Agreed, if we are solely talking about frequencies >7K, as the chance for our brain to distinguish between direct and reflected sound, is pretty low in the upper treble region. There is rarely a necessity to ´tame´ this, as most of speaker+room combinations lead to a decrease in SPL above 7K anyways.
In this particular case, the most obvious difference seems to be located between 3K and 7K (along with lower midrange and deep bass), and I would presume this is also the most audible one. I doubt the imbalance of the solid line speaker would be correctible by just a simple treble control. Risk is pretty high that the lower frequencies of this band (3-5K) will not be sufficiently boosted by such a control, and even if so, the result might be the direct soundfield showing dominant treble (which translates to bright sibilantsand overly brillant timbre) while the reverb still lacks treble. Under the assumption, of course, that a good fraction of the decreasing level towards higher frequencies is caused by directivity and absorption.