As with all things, it depends on the product.
For example, the low-end Behringer mixers like my MX602s have very simple external wall-wart style supplies. They connect to the board with a low-current DIN-style connector, and the big advantage this offers is to make it much cheaper and easier to get the product through its mandatory UL/CSA/<fill-in-the-blank> regulatory testing prior to sale. If the power supply was built in, the whole unit would have to go through the very extensive regulatory screening process for shock hazards, EMI/EMC, leakage, and so on that are required for line-powered units- a very time-consuming and expensive process.
However, if the power supply is external, the unit usually only has to meet the much reduced requirements for battery-operated devices. This is much less expensive, and it puts the onus on passing all the hard requirements on the wallwart manufacturer- so it shifts the costs to them. That's one very potent reason that there are so damned many wallwart-powered products out there: it is a reaction to the current regulatory environment, and it represents a significant cost savings for the manufacturer in the initial introduction of a product. Sometimes that can be the difference between a company making it or not: it's pretty compelling.
Now, in the case of higher-end mixers (like my Soundraft Ghost), the supply is often mounted externally ina rackmount unit, and the final filtered and tightly-regulated supply voltages are coupled over with a fairly hefty supply cable. In that case, the supply is removed from the board's internal environment to move the heat produced someplace else, reduce the overall mass of the board to make it easier to handle, and to make sure that the chances of coupling power supply noise into the audio path are minimized.
You'd really like to have power supplies be located as far as possible from your low-level signal paths. However, going external is _not_ an absolute requirement: it simply makes some things easier, and other things harder. There are a lot of *very* good products with their supplies inside...
In the case of the Ghost, I'm fairly sure that the primary reason to move the supply external was thermal management (it needs a fan to cool it), the secondary issue was reduction of 60Hz power supply noise due to stray magnetic fields from the transformer, and a distant third was weight management (it weighs about 40lb). Since the Ghost also comes in several different configurations, that also allows Soundcraft the ability to send out the right supply for the job without having to gut the box... But even if none of those things were the issue, Soundcraft wanted a higher-quality supply than any wall-wart was likely to provide.
Bottom line if you're a design engineer working on a new spiffy product: if you're going to make a big ticket item, or if you're going to make your own supply anyway, might as well put it in the box (if it fits, and if you can cool it, and if you can lift it all when you're done). But if you're building something that is really cost-sensitive, and you're concerned with either your operating cash or your time-to-market, it'd be worth considering just buying an already-approved wallwart from somebody else, and saving the testing costs and delays....
