Perhaps the question ought to be, 'How could David make a mistake like this?' This was a man who knew God, was open to God and had a amazing 'track record' of obedience.
The Philistines were the most technologically advanced people of those days. Their use of chariots and bronze tools made then almost invincible. The subtle temptations to use modern technology to bring the presence of God into a place have continued for generations.
Perhaps part of the reason for David's failure is that true worship of God had never functioned in his lifetime. The ark was removed from the shrine in Eli's time and not returned until the reign of Solomon. That means that for over 100 years the Levitical priesthood had been disfunctional. They had not taken the blood from the altar and sprinkled it on the Mercy Seat for over a century. There had been no Day of Atonement for over a hundred years. The presence of God had been absent from their 'meetings' for over a hundred years. No one could remember what 'it was like in the old days'.
When we are without the overwhelming sense of God's presence for over a hundred years we become desensitized and hungry for such a 'presence'. This is when we become particularly vulnerable to a 'method' which has worked; remember the 'cart method' had worked for the Philistines, they had moved the ark safely using this method.
How DO we get the ark back into the centre of the nation? Well, it was designed to be carried on the shoulders of people who knew how to wait in the presence of God ie priests. As E M Bounds said all those years ago... men are seeking better methods, God is seeking better men!