Why does writing to a read-only register increase current consumption?
All the other GPIO registers are writable, so I guess somebody just copied+pasted this part of the hardware design, and did not bother to remove the write access.

The PxIN register always shows the current value at the pin. This implies that the register is continuously updated, i.e., the pin always writes to the register.

If you try to write from the CPU, both the CPU and the pin try to write at the same time, which means that both try to drive the same signal as the same time. And if you connect two active driver outputs with opposite levels together, you get a short between VCC and ground. (This short is only for a clock cycle, and through two MOSFETs that do not need to have a low RDS(on), so it's apparently not very harmful.)