Use a oven bag, like one used to roast a turkey for Thanksgiving.
Alternatively, you the double pan method; place the springform pan in a slightly larger pan, then place in bain Marie.
Placeing a pan of water on another rack simply produces steam, and it is not the steam that is needed.
A bain Marie insulates the pans sides from the heat of the oven, slowing the cooking.
Cheesecake has to cook for a long time. Too high heat, too long causes the protein denaturation to happen to fast to the batter in contact with pan. The sides set, but center is still raw and continues to expand.
The cracking will usually happen when the cheesecake is cooling. The set sides are already dried out and firm, but center is still soft and can’t hold.
When the temperature around the batter is regulated, the sides bake slower, do set and dry out before the center bakes.
Water boils at 212°F (100°C) at sea level. Many cheesecake recipes bake at 350°F (170°C).
When water reaches boiling temperature it evaporates and turns to steam. The water cannot get hotter than boiling temperature. So while the oven is 350°F, The temperature around the cheesecake is 212°F.
Placing a pan of water on another rack does not create that insulation around the cheesecake pan.
The other important aspect of cheesecake is a slow cool. I Actually bake my cheesecake at 275°F. When it has a slight brown edge, shut the oven off, crack the door and just leave it 30 min.