Driving a USB-C (video and power) monitor from regular Displayport or HDMI connection from a non-USB C PC?

There are a few display devices available now that use a single USB-C input for both video (Displayport alt mode) and power (USB Power Delivery). However, only devices equipped with the appropriate USB-C port that supports this can utilize them out of the box.

Unlike traditional displays with their own power supplies, you can't just convert one display technology to another (Displayport to HDMI, for example). The source also must provide power, which a typical Displayport or HDMI connection can not do (or at least not enough of it).

Is it possible for a device to exist that accepts an HDMI or Displayport video input, as well as a USB Power Delivery input, and produce the appropriate output to drive this sort of display? I haven't had any luck looking for such a product, so I'm guess either I didn't come up with the right thing to call it, it's too niche for anyone to make, or it violates some specification rendering it impossible to produce legitimately.

Is this something that can/does exist? Or is there a reason why it can't/shouldn't be done?

For reference: This question relates to a wearable device which connects via USB-C, and must be fed a video signal and powered by the device it is connected to. For this device and others like it, the only options to use it (without some intermediate device as described in my question) would be certain phones and laptops which can output video and power via their USB-C port. The question is: is there a existant/possible/permitted configuration which would allow this device to accept a video source from say… A game console, and power from a standard AC adapter.

Okay, so you want a "reverse USB-C docking station" of sorts. Can something like this exist? Absolutely. After all, that's how the USB-C & DisplayPort signal in a PC (or other devices) is produced. There's plenty of USB-C controller chips available with support for Power Delivery and Alt Mode. These could be used to create a circuit that takes USB, power and DisplayPort (HDMI needs to be converted to DisplayPort) and combines it into a USB-C connection.

Does such a thing exist? No, apparently not. This is a quite the niche use case.

Update: I’ve discovered the Wacom Cintiq Pro Link Plus device. It’s for connecting a USB-C pen display to computers that do not have USB-C. It takes power, USB and HDMI/DisplayPort. It’s only $70, so maybe just try it.