If you read back a request to ident and the controller sees nothing on his screen he can reasonably assume that the aircraft has a faulty transponder.
If you do not read back a request to ident and the controller sees nothing on his screen then a whole world of possibilities opens up, from comms failure to a proper nasty, resulting in a lot more comms traffic while he tries to find out.
I was always taught to read back an ident request... and it only occupies the frequency for about 2 seconds.
WD