A couple of disadvantages of triple spool engines (in theory at least) are increase in weight,
Well, theoretically the triple spool is lighter than a twin spool, but for some reason RR couldn't seem to make the RB211-524 lighter than the competition on the B747. However, the triple spool Trent is the lightest engine on the B777 and the Trent1000 is lighter than the GenX.