Brick pillars one foot square will only be stronger than the 4"
timber if steel reinforcing rods are incorporated. I have seen
none re enforced brick pillars simply break off at a low mortar
joint when used in the way you suggest.

4 x 4" timbers at each support point set in a 12" square, well
concreted into the ground with 2"x1" battens forming a lattice
pattern connecting them would offer 10 times the strength of a
single 4" timber post and can be made to look quite attractive.

Mike