Actually why can’t you run PoE as AC? Embedding a high frequency signal on a lower frequency carrier is older than dirt at this point.
At 120 volts, 30 watts is only a quarter amp.
We're just used to power transmission being AC because with AC it's easier to switch large currents on and off, and easier to step voltage up/down.
Right, there will be a voltage where the pins will arc, and a lower potential where a dirty connector will arc.
We rented an office that had previously housed some sort of telecom equipment, so the whole place was wired for, I believe it's 40 volts rackmount equipment. That runs at lower current (thus watts) than computers and so we had to run new electrical and AC into the server room to use it for IT equipment.
Cars are trying to switch to 48V because 40-50V is a range where touching a live wire gets your attention but won't do too much permanent damage (eg kill you). Or if you went with 20v you might be able to reuse equipment designed for USB power supplies.