Why is PoE+ power output 30W?

When the IEEE 802.3at standard was written, it became clear that lead-acid batteries were obsolete. Most applications had turned to the AC-DC power supply. The minimum voltage can be target at 50 V. 

The current was fixed at 600 mA to keep the temperature rise of the cable below 10°C. Note that the cable considered at that time was CAT5e.

Therefore, the minimum guaranteed power was 50V × 0.6A = 30 W. 

The minimum loop resistance of CAT5e cabling was fixed at 12.5 Ω in the 802.3at standard. So the cable loss is 0.6 × 0.6 × 12.5 = 4.5 W.  Then the minimum guaranteed power available to the powered device (PD) is 30W - 4.5W = 25.5 W.

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