I wonder if the brightness and "forward" or "clinical" sounds spoken of are a direct result of the design, or an indirect result.
One thing I've noticed about MTM/D'Appolito designs is that they tend to get the most out of otherswise cheap, unlistenable drivers. I've seen a lot of mediocre tweeters and midrange units aligned in this manner, possibly contributing to results you speak of.

The Seas Froy MKIII model is one of the softest sounding speakers with a wide, and deep 3-d soundstage and certainly doesn't sound forward or bright.

From what I understand, there's been a shift in designs over the decades towards the so-called "forward" sound, for whatever reasons. Creating a more balanced sound, even in a D'Appolito config, shouldn't be difficult, however. I would argue that brightness and "forward" midrange is a failing (or intentional character) of the crossover design (probably low resistor values) rather than aspect of the D'Appolito config itself.

I would disagree with the assessment that mid-range frequencies become linear in a D'Appolito config (at least any more so than any other typical speaker design-we'll leave 'stats and planars out of this for now)...wavelengths of mid-range frequencies are fixed regardless of speaker design or driver alignment, and in the most common 6.5" mid-woofers, you have little to worry about with mids becoming linear as wavelengths approach the size of this relatively large driver. You may be hearing this phenomenon in a room, but it is certainly not unique or attributable to the D'Appolito configuration.