They were designed on ARC. During the 1990s and early 200s their national sales manager used our amps on his speakers; from that its clear the speakers at the time were meant to be an easy load for tube amps.Dave Wilson had some solidstate amplifiers (Ayre monoblock, Parasound and D'Agostino) in his showroom and also in some audio shows but (maybe I am wrong) those solidstate amplifiers were used for powering subwoofers not main towers.
Dave Wilson mainly used VTL (tube amplification) for powering big Wilsons.
I listened to big Wilsons with many different amplifiers but finally I convinced big wilsons are better with tubes
The Watt/Puppy had a famous peak in the midrange/high end due to a resonance in the tweeter. Dave used a 2KHz filter trap to quell the resonance. A trap is a low impedance in parallel with the existing. If you were to use a solid state amp with that the amp would dump power into that trap (where a tube amp would lose power); clearly Dave was designing for tubes and in so doing was not following the 'Voltage driven' rules that govern most speaker designs.