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

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.  

The proper size cabinet for a 15 inch woofer is LARGE! I had a pair of vintage JBL C36's with the 2215 woofers. These had the "James B. Lansing Signature" logo on the top front edge.

It depends what waveguide is used (SEOS?). However, it is very hard to get a 1” tweeter/compression driver to blend with an 8” without having increased directivity (narrower soundstage, and maybe worse imaging). Unless using a super waveguide, I wouldn’t use a midrange larger than 5.5”.