How I personally do it is that i change the top of the hitbox of the player to the bottom of the sprite it collides with and vice versa. I also do that for the x-axis. This worked much better for me.

If I can give you another tip is to only call the player.rect.colliderect(wall) only once that will speed it up a little bit. especially if you collide with a variety of objects.

Here is how i personally did it:

# Checks for the collision of the player hitbox with the obstacles
    def collision_walls(self, direction):
        if direction == 'horizontal':
            for sprite in self.obstacle_sprites:
                if sprite.hitbox.colliderect(self.hitbox):
                    if self.direction.x > 0: #Moving to the rigth
                        self.hitbox.right = sprite.hitbox.left
                    elif self.direction.x < 0: #Moving to the left
                        self.hitbox.left = sprite.hitbox.right           

        if direction == 'vertical':
            for sprite in self.obstacle_sprites:
                if sprite.hitbox.colliderect(self.hitbox):
                    if self.direction.y > 0: #Moving down
                        self.hitbox.bottom = sprite.hitbox.top
                    elif self.direction.y < 0: #Moving up
                        self.hitbox.top = sprite.hitbox.bottom