Hexes are trash because you can't conveniently navigate a hex grid using a numpad. However, diagonals on a square grid also cannot have the same move cost as orthogonal moves without making orthogonal movement borderline obsolete. Even in extremely simplified movement systems, the fact that diagonals are simply, literally more distant creates all sorts of advantages for always moving diagonally.

Take pic related for example, you want to move a unit up on a grid by two spaces, in as few moves as possible. Orthogonally (blue player) you have the sole option of moving up in a straight line, twice. Meanwhile diagonal movement (red player), by virtue of traveling a longer distance with each move, offers two route choices, twice as many. Diagonal movement is thus demonstrated as strictly better by virtue of giving the player more options. An obstacle on one route can be avoided by taking the other route, and you have twice as many chances for a secondary objective to appear on one of your routes because there are twice as many. Meanwhile, an obstacle in the center route means an orthogonal mover would need to make two additional moves to circumvent it, doubling the total duration to the finish where diagonal movement would have suffered no delay whatsoever. This level of divergence in player capability emerged in TWO GRID MOVES. Now imagine what happens when this advantage compounds over hundreds, if not thousands, of moves in the course of a longer game. Winning will almost certainly correlate with who moves diagonally more often before anything else, if movement in your game matters at all.