We spend too much time talking about tweeters

kingharold is correct. Music is in octaves. If one considers the 3.5 kHz crossover, in a two-way system, the woofer then covers 7-1/2 octaves! If there is a midrange speaker crossing over from a woofer at say 250 Hz, the woofer then covers about 4 octaves, while the midrange covers about 3.5 octaves before crossing over at 3.5 kHz.

As audiokinesis posts, the ear is most sensitive over 700 to 7000Hz range, with the most sensitive in the ~1-3 kHz zone. It then makes sense to have a very good midrange speaker crossed over below 500 Hz and maybe above 8 kHz, ballpark frequencies, so that the most sensitive hearing range has no crossovers at all, so no large phase transitions over that range.

This is a design problem with compromises galore.

my point was never that we should ignore the high frequencies, but that we talk about tweeters like they are the whole speaker.

Speaking of using a 3 way, I have to say I'm really intrigued by the idea of a woofer-assisted wide band.  It's almost like a full-range, with a woofer added. Could be pretty interesting, but like Duke, I don't find crossovers to be nearly the villains they are made out to be.

Recently had a tweeter go bad in one of my speakers.  I picked a replacement up off eBay and it was worse than the original one that went bad.  Ended up buying a new one from a reputable source.
The tweeter may not produce most of the sound but when they go bad it makes everything sound like crap.

Something noticed about my AMT's is that 'played ' without a bass speaker of any size sounds like strangling a small animal...and they go down to +/- 500hz.....
Matching the 'speed' of an AMT (or a ribbon, small planars, and the like) almost requires crossing over to a smaller woofer properly.  Hand over the sub-150hz and below to a decent sized sub to 'move' substantial amounts of air about....
I've found that adding a smaller (and lighter) Walsh to my larger ones makes a substantial difference to their response and to the general perceived 'air' from them.  'Uncoupling' the 'top' fq radiator and using a smaller voice coil (contrary to the design of the F's and A's of the past) may be heresy but it does seem to work well.
(I'm not using a typical 'enclosure' with the larger Walsh unlike Ohms', new or old.  Just a sealed tube; think 'acoustic suspension', to damp excursion...).
The Tweet Matters, basically.  But what's 'below' completes the 'image'. ;)

Nobody has quoted the immortal lyrics of Meghan Trainor:
I’m all ‘bout that bass, ‘bout that bass, no treble...
i can shake it like I’m supposed to, cause I got the boom boom that all the boys chase...

What is wrong with your people?!