Why do modern jousters use draft horses?

Because, to be honest, we've mostly lost the "great horse" or "destrier."

Draft horses are often the only animals that can handle the weight of 100 pounds of armor plus maybe 150-200 pounds of jouster plus the weight of the barding. They are also mostly (but not always) easy to desensitize to crowd noise, rattling armor, etc.

Ring jousters and some jousters who "fake" it at RenFaires often use lighter horses.