I think that the opinions of CDAs will rather depend on where a pilot has experienced them! The flight-idle-to-1000ft proponents are obviously not regulars at Heathrow, which mandates CDAs but effectively imposes gate heights and speeds which demand speed/vs autopilot modes thereafter (the gates are too low and slow to allow a flight idle descent).
CDAs of any variety are fairly easy to achieve as long as the pilot is given a reasonable degree of freedom over descent points and/or speed. To achieve the FI to 1000ft profile at an airfield with arrivals from all directions is going to be difficult without gates to focus the arrivals, but those gates must correspond with a power-off profile for the majority of likely arriving aircraft. Radar vectoring at any point in the arrival makes it more difficult for the pilot to judge the CDA profile, as he's effectively got to guess how far the controller's going to take him, so CDA arrivals should follow the published arrival track wherever possible (almost never at LHR!). At LHR, with the variables introduced by the controlling methods used (which I'm not complaining about), it's amazing so many pilots manage to achieve a more-or-less CDA (from the hold fix) at all!