Phased Antenna Array Directivity
Generally, the directivity of an antenna or array does not depend on \$P\$ or \$P/n\$.

The main contributor to directivity is \$L\$, the diameter of the array. The advantage of a phased array is that the array diameter can often be much larger than the diameter of any individual element. For example, one element can be in Hawaii and the other one in the Virgin Islands, giving an array diameter of 8000 km for the Very Long Baseline Array, with angular resolution around 10 micro-arcseconds.