The account of Uzzah's death was written to "teach us" something - to warn us.(Romans 15:4; 1 Corinthians 10:11) That is where we have the advantage - learning a lesson from the drastic mistake of others.
Something to take note of is how the oxen that pulled the new cart with the ark in it stumbled on a flat surface - a "threshing floor".(2 Samuel 6:6) This should raise a red flag in the reader's mind. If the oxen had stumbled on a rocky surface, we could consider the terrain as a cause. What is wrong with this picture? What does Scripture say? The ark was supposed to be covered in a specific way, and "the Kohathites" were supposed to carry it with poles.(Exodus 37:5; Numbers 4:5-6; Numbers 4:15) So their means of transportation was an act of disobedience against God because the instructions were written on the scroll. Look at the warning for the Kohathites in Numbers 4:15: "But they must not touch the holy things or they will die."
So where did the Israelites get the idea that they could transport the ark of the covenant on a cart in the first place? After the Philistines captured the ark of the covenant, they were afflicted with plagues of tumors and rats wherever the ark went - "the outcry of [Ekron] went up to heaven."(1 Samuel 5:12) It was decided that the ark should be sent back to Israel. According to the instruction of their "priests and the diviners", a "new cart" was built to transport the ark.(1 Samuel 6:2,7) The Israelites, who were bound by the law of God written on the scroll, should not have used the same means of transportation as the Philistines who acted in ignorance.