Sure you can use but if you think it why it might be a bad idea you don't really want to.
Because most power producing devices already have plugs and power consuming devices have sockets, that's the current de facto usage and infrastructure you live in.
If you do make a socket as an outlet,
it allows you to make incorrect connections and damage something.
If you connect the power supply to your inlet because the connectors are near each other, will it damage something? If you accidentally plug in incorrect plug and you parallel two power supplies, will they damage?
Also there are not that many cables wth DC plugs on both ends that you can buy. That's because usually you don't have the need to connect two devices together from their sockets.
It isn't that mind-boggling at all. And we have many questions if it is a good idea to use standard connector X for custom purpose Y, and most of the time it isn't.
You can use any connector in any way you want, there is no rule or law against it, except common sense to limit use to the de facto usage.
If you use the DC jack to provide power, it allows accidentally damaging something.
Much like you decided it is a good idea to transfer mains power to a bike shed with a cable that has mains plugs on both ends.
Same goes for using USB connectors for non-USB usage. Not a good idea. You or someone else will damage a standard USB device like PC or mobile phone if accidentally plugged in, just because a matching cable looks to be free to use for charging.
There are already too many different and incompatible uses for connectors like 8P8C modular jacks (some people call them RJ45), XLR connectors, TRS plugs and jacks, DIN connectors, D-Sub connectors etc. You can't expect devices to work or even survive without damage when plugged in, even if they have matching connectors.
There are many standards that have mandated which connector to use and how. Some standards (like DMX512, AES/EBU, MIDI, RS-232) have defined to use existing connectors used also for other purposes. Some standards define their own connector (USB, HDMI, DisplayPort) that have not been previously used for any purposes, which guarantees they are used by engineers as per the standard, and there is the assumption it is not used incorrectly to incompatible non-standard purposes.
Some receptacles like HDMI and DisplayPort are identical on monitors and PCs, and the assumption is, you will use a cable with identical plugs on both ends to connect a monitor to a PC, as you would know from the context that it makes no sense to connect two monitors or two PCs together even if the connectors allow it, and the interfaces are designed to not damage if accidentally connected incorrectly.
With USB Type-A and Type-B, standard mandates what kind of connectors are used on hosts and devices, and what kind of cables are defined to be used between them. So as hosts have Type-A sockets and devices have Type-B sockets, you know you only need cables with Type-A plug and Type-B plugs, and it alone prevents from making invalid connections that do damage, as you have no cables to connect two hosts or two devices together.
USB Type-C is different. All your devices have same receptacle, much like HDMI or DisplayPort. Cables can have same Type-C plug on both ends. The standard requires that even before power or data wires are activated on the receptacle, the devices must negotiate their power and data role. For example you can plug in two laptops together, but likely it makes no sense during the negotiation process and nothing happens. Some laptops may allow to start charging the other laptop. But any invalid combination or unsupported role on a device will just do nothing.
That does not apply to your DC plug. 99.99% of the devices are built with the assumption plugs provide power into a receptacle, and cables with plugs on both ends are not needed for that reason.
DC plugs are already a hazard as same plug and receptacle is used for different incompatible voltages and currents. It's already a pain to make sure you are not plugging in a 12V supply into a 5V device, or 12V supply into a 12V device which expects different DC polarity.
So while you can use a receptacle to output power, nobody expects it, and there is no existing infrastructure to support that, such as cables with DC plugs on both ends.