Yes that is true and it's a convenient method that I rely on when making one-off speciality devices. I have to say that I am generally a fan of external power supply units. There can be advantages in keeping the PSU heat, volume, weight and electrical noise out of the product itself. Also in the (surprisingly rare) event of failure, wall warts can be easily and cheaply replaced without having to send the gadget away for repair. There was almost a whole industry dedicated to reparing the small SMPSUs in early digiboxes that were notoriously unreliable, which would have been avoided had the PSUs been external. Yes they can cause socket clutter but how serious is that really? I can live with a bunch of wall warts under the 'gadget table' in the lounge but if the gadgets had integral power supplies they would be larger and wouldn't all fit on the table.
I have a specific reason to favour external PSUs in my particular line of electronic work, because they allow me to modify and improve power configurations when integrating hardware into a system, without hacking and invalidating warranties on the products themselves. For example, my portable media capture & processing systems are designed to operate from external Li-Ion battery packs or mains. I build a custom multi-input, multi output power supply chassis that powers a dozen or more separate products at 5, 12 and 48V and gives UPS functionality if a battery is left connected while on mains. It combines low noise, very high reliability (sometimes dual redundancy) monitoring and control in a convenient, all-ELV chassis. The mains input goes via two or three 19V 240W medical grade level VI power bricks that can be hot-swapped, so I keep the mains out of my own power chassis too. If the powered devices were mains-fed, an inverter would be needed which is less efficient, typically less reliable, acoustically noisier, tends to produce horrendous electrical noise (HF inverter) and/or adds serious weight and bulk (LF inverter.) Otherwise I would need to open and void the warranty on dozens of pieces of gear costing up to £5,000 each to bypass the internal PSUs.