Summary: Cost, reliability, convenience and certification of the assembly with the device.
USB-C Power Delivery seeks to overcome these issues while offering a demountable cable.
An additional connector adds cost. That said, the arguably most common power adapter type on the planet - USB - has a detachable supply-side connector. USB is mature and highly cost-reduced, and most important, standardized, so it can get away with this. Not so for a laptop brick.
Nevertheless, USB-C PD power bricks with detachable cords are a thing now, at least for Macs. They do cost more though.
The DC side connector has to be rated for high enough current to handle the load. Connectors oxidize, have limited mating cycles and thus can fail over time. The typical barrel type connector is very rugged and is designed for a large number of mating cycles. On the other hand, an additional supply-side connector is an additional failure point.
It remains to be seen how rugged USB-C PD will be compared to a barrel connector. I consider it kind of fragile.
It may seem ironic that having an attached DC cable on the laptop brick is convenient, but it is. Experience bears this out: in our household we always seem to be one USB cable short of the one we need, at the moment we need it. The laptop power cables never get waylaid in some drawer or glovebox because they’re part of the brick.
USB-C, if it becomes as universal as USB-A, can completely overcome this issue for laptop-capable power supplies. While you still can find yourself without a cable or an adapter at an inopportune time, at least USB-C solutions are somewhat easier to get than a proprietary laptop cable+brick.
Example: I've already invested in a 12V to USB-C PD car adapter so my better half can use her Mac on the go. On a recent road trip I was able to walk into a Staples and get one (and pay too much for it, because, you know, Staples.) Works great, we'll see how it holds up over time.
EMI/EMC Certification of the Assembly
The brick you show has an additional ferrite bead at the device end. This is a hint that the device it's powering had issues with conducted electromagnetic interference (EMI), so the manufacturer had to resort to that ugly add-on fix to suppress it. It could also be to suppress fast-transient spikes coming from the power supply to the device. Or it could be doing both things.
Really, EMI issues should be addressed in the device itself using a common-mode filter, but they chose to do this instead on the attached cord. If the cord were detachable this would defeat the EMI workaround.
Speaking of which... a USB-C PD brick and laptop must deal with these issues internally. They have to for interchangeability. This would imply a USB-C PD brick and device would be better-designed for EMI/EMC than a dedicated brick.
My shiny-new Lenovo laptop arrived. It uses a USB-C power cable, that is permanently attached to its power brick. At least I can charge the laptop with that Staples gizmo.