Class-AB amplifiers offer the lower cost and cooler operation of class-B, with some of the finesse and high fidelity of class-A.
You get the best of both worlds here, but only up to a point. Class-B operation is not good for audio because of non-linearity around the output device crossover point, resulting in crossover distortion. Class-B designs offer more power, lower weight and lower cost than a class-A design of similar power, but they are a brute force design. Class-A amplifiers have no crossover distortion but are heavy and run hot, even for very modest power outputs, because they run at their rated power, all the time, even with no signal.
Class-AB amplifiers operate in class-A up to a few Watts and then revert to class-B for the rest of the power envelope. At lower levels, you’ll have the sweet sound of class-A. You’ll have the punch of class-B for dynamic swings and higher volumes. The more class-A power on hand, the better the sound, because the more of the envelope is reproduced via class-A operation, other things being equal.
Almost all consumer-grade amplifiers operate in class-AB because of this design topology’s cost-effective yet relatively high-fidelity nature. That being said, most consumer amplifiers run very little class-A power, sometimes only a couple of Watts, or less!