How safe is 48V DC?
frankly the difference between 48V and 120V doesn't seem to be that significant.
120V is 2.4 times higher than 48V - hardly what I would call 'not that significant'. 120VAC is even worse, for two reasons:-
120VAC has a peak voltage of 170V, 3.5 times higher than 48VDC.
The 'electric shock' feeling occurs on every peak of the AC waveform, whereas with DC it mostly occurs on initial contact.
It only takes about 30mA of 60Hz AC current through the heart to cause fibrillation, compared to 300-500mA of DC current. The 'let go' current (above which you cannot let go of a grasped conductor) is 4 times higher for DC than AC. So that means you need 4-17 times more DC voltage to get a fatal shock.
Combine 2.4 times higher voltage with 4-17 times higher susceptibility, and 120VAC is approximately 10-40 times more deadly than 48VDC.
But is 48VDC safe in an Ethernet cable? Provided you don't strip off the insulation and poke the bare wires into your flesh, the chances of getting a fatal electric shock from it are negligible. I know from personal experience because I was a telephone exchange technician for 15 years, and regularly worked on live equipment with exposed contacts. The biggest DC shock I ever got was a light tingle when grasping a 50V bus bar (90VAC ringing was a different story...).
48V is the practical and LEGAL definition of the maximum voltage to be considered "low voltage" and intrinsically "safe". Certainly 48V delivered UNDER your relatively insulating skin surface could kill you if delivered in the "right" place. But we are assuming people aren't walking around with subcutaneous electrodes exposed to accidental contact with "LV" wiring. 48V is reasonably safe for most people under normal conditions.
As observed by @crowie, the original (and current) technology wired public telephone system operates on 48V for over 100 years. That old telephone technology is very likely the precedent for establishing 48V as the legal limit.
No death by electrocution going to happen
48V is considered "safe", and that is for good reason.
First, the impedance of the human body at 50V is around 45kΩ (though measured on adults). While children are overall smaller and thus should have slightly lower impedance, it's the skin resistance which makes up 95% of that impedance (internal body fluids are pretty good conductors), so the size doesn't matter all that much.
(Note how body impedance is a funny thing, it goes down rapidly as voltage goes up, at 240V it's 10-15 times lower!)
Further, an electric current needs somewhere to go, obviously. No closed circuit, no current. That's why birds sitting on an overland line aren't fried.
These 48V are 48V against ground. In all likelihood, the next closest thing to "ground" that you have contact with is "parquet/laminate" or "floor tiles" or something similar, in other words, resistance around infinite, current zero.
Even touching the hot wire on 240V has a good chance of "not much bad stuff happening", if you wear shoes and aren't precisely standing in a puddle of water (although for obvious reasons I wouldn't advise trying your luck!).
Let's assume the absolutely worst case: a child puts one finger onto the ground pin on a wall plug, and sucks on the PoE cable (looks edible, doesn't it!). Against all odds, the PSE is broken or heftily non-compliant and instead of supplying 10.2V/4mA max as per default, it supplies full operational voltage, and unlimited current. Or, it takes some random pattern that the child accidentially made for a valid negotiation, whatever.
Also, for an unexplainable reason, the current doesn't short circuit over the data wires (the likely thing to happen would be exactly that, a little spark on the child's tongue, and the child dropping the cable in a fright).
Let's just say there's actually 40V on the wire, and the current "decides" to go through the child's body, against all reason and against the laws of physics.
Cable-in-mouth will eliminate one skin barrier and thus approximately halve the body impedance. That's 22.5kΩ remaining. Let's round down to 20kΩ to be sure. No, you know what, let's be outrageous, and say 10kΩ. 48V/10kΩ = 4.8mA.
Which... is harmless even for alternating current. It takes about 8-10 times as much alternating current (of a frequency in the critical 50-60Hz range) to stop the heart.
Now, on top of that, PoE doesn't have alternating current, it's DC. So the scary bit about cardiac arrest doesn't even apply.
Of course, DC can in principle cause adverse effects other than stopping the heart (think of a surgical electro knife, or the "electric chair"), but given voltages in the two digit range and currents in the single-digit milliampere range, this simply isn't going to happen (but even if it was, it would primarily be local burns, not life threatening).