Driver heads are huge, but I still see plenty of heel and toe hits. The reason? Most golfers swing it too hard, with either the hands and arms or the hips racing out of sequence on the downswing. Either way, the club gets re-routed, leading to off-centre contact. If you pull the club down from the top with your hands and arms, you move it away from your body which causes a heel hit because the club swings across the ball from outside the line. To fix this the club must be kept to the inside.
Close your stance, and focus on hitting the inside of the ball, swinging to the right. If you slide your hips aggressively towards the target to start the downswing, the club can drop too far to the inside - known as 'getting stuck'. If causes contact on the toe. To stop these, you have to get your arms back in front of your body sooner. Try to make a smoother transition with your lower body. Remember, making good contact is the key. More speed means nothng if you don't hit it flush.
Focus on hitting the inside portion of the ball, and swinging out to the right.
Making a smoother downswing transition with your lower body is one way to avoid "getting stuck" and hitting it off the toe.