Out of most of the electronics I use, I have two, both of them speakers, that use a power adapter that simply steps down the voltage without rectifying it. Why did the designers choose to put the rectification circuitry in the speaker instead of the power adapter?
One reason is that you usually need positive and negative voltage for audio amplifier. (Like +5, 0, -5 V).
Another reason: Some devices run directly on AC, e.g. Christmas light bulbs can do.
Yet another reason: Some devices need two different voltages, like 5 V and 12 V.
Yet another reason: An external step down transformer provides just safety. Voltages no higher than 50 V are usually accepted as safe (although not very safe with high current). So the transformer makes it safe, the rest is in the device.
There could be any number of reasons it was done the way it was, and only the designers have those answers. Some possible scenarios:
A suitable transformer may not fit inside the device's enclosure.
In testing, the magnetic fields from the transformer may have caused unacceptable audible artifacts.
The transformer wall warts were cheaper than a chasis or PCB mount transformer.
It can be two things, and since it's audio, probably both. The first, most electronic device companies specialize in one thing, the main product they sell. They tend not to get into the highly annoying area of power supplies. Their engineers figure out what voltage/current/quality power supply they need, and then they buy generics bulk from a Power Supply manufacturer (often paying extra for custom labeling or tighter quality control). It's just way cheaper that way.
The second thing would be, especially in audio devices, additional quality control. Might cost 10 cents for a ac to dc power supply compared to 5 cents to put in a rectifying stage inside the speakers while providing better rectifying control (eliminating cheap wall wart rippling or ground loop issues, shorter signal/power/trace lengths to deter emi etc), they will do it. The power supply manufacturer(s) might not have a cost-effective standard part with a quality dc output.