Because it is not a power cable (Q1) using power connectors (Q2).
BNC cable has a solid conductor and a ground braid to electrically shield and mechanically protect the conductor.
Electrical reason: Some ground braids are made of steel, which is not as good a conductor as copper, so voltage losses to the wire would be higher than copper wire. Basically, wasted power.
Current creates heat ($I^2 R$ losses). The ampacity rating of a power cable is determined by the maximum temperature the cable's insulation can handle. The BNC wire was never meant to carry power, so the current flowing may cause the insulation to break down and cause a fire.
Safety reason: The main reason BNC cable should not be used to send power is because of the connectors. The outside of the metal BNC connector is uninsulated, so you have a shock risk, if you disconnect the load terminal while power is being applied.
Common sense reason: You may know what you have done so are not at risk, but an unsuspecting person is NOT expecting power on a signal cable.
Even if you found an insulated BNC connector and added a warning sign, if it was disconnected a user may connect a normal connector negating your bad practice.
From: Generic BNC Male Connector UHF Walkie Talkie Antenna 2.8 Inch For Kenwood TK-388
No one expects power over a BNC cable. So power distribution over BNC cables is bad practice.