Perhaps someone "In the know" could elaborate how much power is required for these transients in the bass region.
The recording is the driver of power levels, look to the waveform for the initial clues.
The waveform represents the request for voltage from the amplifier by the recording to be applied to the speaker terminals.
As for "bass transients", uh, there aren't any. Bass is slow slow slow.
In the organ piece above, here is the highest voltage request. Ooh... looks like an abrupt change, and hard to reproduce... The clip is about 2 milliseconds in length.
Let's call that peak 50V. Loud. 625Watts into 4 ohms load loud.
Now zoom in on that "transient". The dots are sample values, and are 0.000023 seconds apart - 23 microseconds.
The slew rate - rate at which an amplifier can change voltage - "Most well designed amplifiers are flat out to 100kHz so in that case you would need a minimum slew rate of about 32V/usec in order to achieve such a wide bandwidth". -
https://www.audioholics.com/audio-amplifier/amplifier-slew-rate
So, for this example, assuming 50V peak of the music waveform, might need to move 2 or 3 volts in 23 uS, well below its capability.
There are faster transients, none should really tax a decent amplifier's ability to follow the waveform, if the amplifier's bandwidth exceeds the bandwidth of the musical signal, and it can flow current as demanded by the load at the requested voltage.