nearly every vintage speaker I have heard sounds coloured, has flabby bass, and limited in both frequency extremes
If that's all you've heard, then I submit you haven't heard a properly set up vintage system. The key element here is enclosure size. Many of the better drivers from Altec, E-V, JBL and other were designs to sound best in really large or even infinite baffle type enclosures. I'm talking about cabinets with 15 cu. ft. or greater volume. As a practical matter most manufacturers ended up making many models in smaller, less optimal cabinets and tailored the bass response to sound bassy as opposed to accurate. Examples of vintage speakers with truly great bass extension and performance are Bozak Concert Grands or E-V Georgians/Patricians.
Many of the better vintage manufacturers came out of the movie theater industry and made their names producing speakers that were very large, went very loud and could project their sound in a controlled manner throughout a large area. I know many people love their VOTTs, but I just don't think they sound right in normal size and styled listening rooms. What these speakers can do extremely well is midrange frequencies. Voices, arguably the toughest instrument to get right, can sound very real on these type of speakers.
IMO modern designs clearly have a more extended treble than vintage. It's a debatable point whether this is truly critical or not.
Classical Audio Reproduction, a fine Michigan company, manufactures loudspeakers based upon vintage design, but uses modern materials. I wouldn't say they are better than competing, more modern based designs, but they certainly are competitive with them.
