Seriously? You better believe it. Real life sounds have sharp, high transient peaks that seem like no big deal but require massive power to faithfully duplicate in a sound reproduction system. The amplifier has to generate sufficient power to overcome the mechanical and electrical inertia of the speaker drivers to make the slap of a drum or pluck of a string sound real. The more power on tap in the amp, the more realistic the sound. That's why amplifiers have big transformers and capacitors, so they can hit those momentary high Wattage peaks if just for 10 ms or so. Not 14,000 Watts probably, but 3000 Watts is possible for a very short time. That power is needed to make the fast rise times so the music doesn't sound blurred or distorted. That's the difference between listening to a hifi system and a clock radio. For sure, the transistors will pop like fuses if they have high current levels for too long. It is all about heat buildup inside the semi-conductors. His amp manufacturer rates the transistors for 60 amps, but no idea if that is for 1ms or 1 hour. The circuits may be capable of those power levels, as I am thinking for robustness, but agreed the amp could never generate those power levels for more than milliseconds (and likely not 60 amps) being supplied by a standard 120VAC wall plug.
One example that comes to mind is the 1812 Overture. I have never heard the cannons faithfully reproduced by a stereo system. The power to do it would be at the industrial level, as well as the speakers to handle that sound pressure level. I mean you know they are cannons that are being fired, but not even close to the impact and shear power of the real cannon shot. I think it would be fun to play the record and have someone fire real cannons at the appropriate moments, but the neighbors might not think it so much fun.