I missed this earlier.
Imagine a volume control, and a pair of magically-fast fingers which can turn the volume control up or down as fast as necessary, even thousands of times a second.
Let's consider what you called "AC compression". If we have a 1 kHz sine wave coming in, and use our magic fingers to twiddle the volume control up and down 2000 times a second, so as to flatten both positive and negative signal peaks, we have what you called AC compression.
But what we have done is alter the waveform of the signal - flat-topped the individual peaks. The human ear/brain perceives this as harmonic distortion. The sound will be harsh and distorted.
Most singers, violinists, pianists, cellists do not want to sound like an electric guitar in Jimi Hendrix' hands - we do not want harsh distortion added to our music signal.
So twiddling the gain pot as fast as the individual half-cycles of the incoming signal is out, except for guitar fuzz-boxes, overdrive pedals, and so on, where large amounts of harsh harmonic distortion have become acceptable. A very fast-responding compressor signal causes harsh harmonic distortion, so it cannot be used in most situations.
Suppose instead we twiddle the gain pot quite slowly, using normal human fingers. Suppose we turn the gain up and down at the rate of only once per second, lowering it when the signal is too loud, turning it up when the signal is too soft.
Now there will be a thousand cycles of a 1 kHz waveform during the 1 second we took to raise or lower the gain. Each individual cycle will barely be affected, so the waveform doesn't change perceptibly, and we don't hear distortion. If we're good at it, we can maintain a somewhat steady average level.
Unfortunately, if a sudden loud spike comes along - a loud drum-hit, a vigorous pluck of a guitar string - it will burst through to the output long before our fingers respond (a second later) and turn the volume down.
So a very slow control signal won't cause lots of THD, but it also won't stop sudden changes in signal level, which will get through the compressor before it has time to respond.
This is the conundrum of compressor design. If the attack and decay times are extremely fast, you get harsh distortion. Slow them down a bit, you get thumping and popping. Slow them down some more, and loud peaks aren't compressed at all!
There is no perfect solution - all compressor design is compromise. Ideally, we would manage to control the envelope of the waveform, without messing up individual signal peaks. And that is an impossible challenge, at least if we're speaking about real-time.
Working with an already recorded signal (or one that's been delayed by a DSP chip), computer software can "look ahead" to peaks that haven't arrived yet, and get ready to respond to them. This lets software / firmware do a much better job - it has time to respond to peaks before they actually hit. This sort of "look ahead" compression can do a much better job than old-fashioned analogue compressors do.
An analogy would be the cruise control in your car, which is clueless about that upcoming hill, so it always waits too long to actually start depressing the gas pedal - it has to wait until the car begins to slow down, which is the only clue it has to operate on.
You, on the other hand, using your eyes, can see that hill before your car reaches it, and you can start to roll your toes into your gas pedal before the car actually begins to slow down. You're a "look ahead cruise control".
(But look-ahead compressors are not ideal for live performance, because they have to delay the signal by at least several milliseconds, and this can be extremely problematic for musicians, who have to listen to themselves in order to play accurately and on-time.)
-Gnobuddy