Do multimedia speaker systems run on AC power rather than DC?
The answer to "why is it made this way?" is quite often "it was five cents cheaper to make."

The audio amps always run on DC.

Modern multimedia loudspeakers would probably use a Class D chip requiring a single positive supply, powered by a switching wall wart.

Older chips require a symmetric power supply (like +15V and -15V) or a single supply if they are bridged.

This presents a problem...

Getting a product certified for safety is expensive if it has a mains input and mains voltage inside. It is cheaper to use an AC adapter which is already certified. The same adapter can be used for lots of different products. If the AC adapter is made by a specialized manufacturer, certification costs will be spread even more. When using an AC adapter, what is removed from the product enclosure itself is cost, and this cost lies on the mains voltage AC side.

An adapter also removes heat from the enclosure, and .. heat also makes the device cost more, makes it bigger, etc. An ugly wall wart is the match made in heaven for every modern sleek and thin device ...

While it would be possible to use an AC adapter providing a symmetric +/- supply, this would make the adapter more specialized, thus harder to sell for the company which manufactures it. It would need a 3 pin connector, again more expensive and less standard than a DC barrel connector. 

All this means that, if you want a +/- symmetric supply, an AC adapter which outputs AC is a good solution. The device being powered will contain a rectifier (two half-wave rectifiers) and capacitors to make positive and negative DC. This has more ripple than a transformer with proper full-wave rectification, but for cheapo multimedia speakers, no-one cares.

Even if the amplifier only requires one positive supply, you want low impedance between the supply caps and the amplifier circuit, which means the caps should be in the device, not in the adapter. And you don't want to pay for caps in two different places when you can pay for just one! Every cent counts.

Switching supplies make up for this by being cheaper and lighter (thus cheaper to transport and sell) than transformers...

...but they are a specialist job, and EMI certification is expensive, so your average tech equipment manufacturer will either outsource or purchase from a specialized manufacturer. And this is how you get a super thin sleek flat TV with a big fat power brick.