inherent design flaws with a 3 way, 15" / 8" / horn (large tower) speaker?

Your premise is flawed.  There are many, myself included, who consider a 2-way or 3-way with 15” vintage paper cone woofer to be more musical than a 2-way bookshelf or slim modern speaker.  The key is the “vintage paper cone” part.  These woofers have little in common with a modern era 15” woofer with a heavy synthetic cone. The vintage woofer is more efficient (99 dB for example) and super-fast; it can blend seamlessly with a lightning fast horn/compression driver.  Forget the 8” driver in your example.  A good vintage woofer can easily cross over to a horn at 800 or 1200 Hz.  Having a driver in between would simply make the sound less coherent, less seamless.

So why aren’t speakers with a 15” woofer and big horn more common today?  Size is the main reason.  The woofer is big, the cabinet for the woofer is much bigger than normal today, and the horn is also big.  And then you need a pair for stereo.  But for those who have the room to accommodate a pair of large speakers, this is the way to go in my opinion.

thank you for a great response.  i did order a pair of car audio 15"s as an experiment.  Ultimately I would love to decipher the hundreds of jbl driver model numbers and find something "new but vintage" to drive these speakers. crossover to sub at 80 or 100hz and to the mid at around 550hz. if i can find an 8 that is sufficiently musical from 550-1850 hz (horn-dependent) ill hand it over there (1850 or so). ultimately diy second order crossovers MAX (a great speaker imo should hand over frequencies gracefully back and forth to the correct drivers)
withering feedback welcomed within reason

The Classic Audio Loudspeaker models T-1 and T-3 seem to be set up this way. They sound great- one of the most transparent and musical speakers I've heard.

As I was looking at DIY speaker kits I see that large paper cone woofers are still popular in parts of that market. Some of these kits are pricey too.

Two examples of the woofers I was talking about are the Altec 416 and Jensen P15LL.  My two pairs of speakers each use the P15LL which is a high efficiency 15” with light paper cone and an Alnico magnet.  It was used in the Jensen Imperial horn speaker as well as other commercial units back in the 1950s and 60s.  Both the Jensen and Altec are available on EBay.  In addition Great Plains Audio makes new Altec speakers using the same design and materials as the originals.

There are many horns and compression drivers that can blend nicely with the woofers.  For a number of years I used an Altec 32B horn with 802-8G driver with a 1200 Hz crossover.  I now use a YL Acoustic horn and driver with an 800 Hz crossover.  Both speakers are pictured in my system page.  Each of these is a great sounding, high efficiency (99 dB) speaker that is an easy16 ohm load for a tube amp.