During hydrolysis of a halide of carbon via $\mathrm{S_N2}$ mechanism, the incoming neutral water molecule attacks the partially positive carbon centre from the side opposite to the halide side and forms a transition state where the hybridisation of centre is $\mathrm{sp^2}$. The nucleophile and the leaving group (halide) thus are attached to opposite sides of the same p orbital (now elongated). Ultimately the nucleophile kicks off the halide from the back.
But when we are carrying hydrolysis on $\ce{PCl3}$ (phosphorus trichloride) why does the water attack an empty d-orbital of the central phosphorus atom and not do the same mechanism as it does in the previous case mentioned. Why can't the attack take place like above leading to formation of an elongated p orbital?