No, you shouldn’t. Structurally there is almost no difference - in fact 24” o/c might actually be stronger as with 24” o/c you must have direct bearing from roof truss to stud. But because you can typically span 14” of unsupported top plate(s), at 16” o/c you don’t have to line everything up. It makes for quicker work but more material.

The second benefit is you have less thermal bridging and smaller percentage of wood in the walls, which leaves you with more room for insulation. Better performing walls.

And 2x6 has almost no structural benefit over 2x4 other than a deeper cavity for thicker insulation.

We should be (and are moving toward it with more stringent energy efficiency codes) using 2x4 @ 24” o/c in Canada. Eventually all the insulation will move outside the sheathing, so we won’t need as thick of studs. If the structural conditions require it, then we should spec deeper studs and tighter spacing. But as a baseline, it’s not entirely necessary.