why do true katydids sing only at night and no other time?

Answer 1

Simply because they are a nocturnal insect:
"Katydids eat the leaves of many trees and shrubs. They stay motionless among the leaves during the day and feed around sunset. Male katydids "sing" to attract mates by raising their forewings and scraping a rigid edge of the right wing against a filelike section on the left wing--a process called stridulating."

http://www.dnr.state.mn.us/volunteer/julaug00/katydids.html

Answer 2

because they just do