Hi fmgc. Standby for some feedback from current controllers. meanwhile... there isn't strictly a "SATCO Luton Approach". The approach function is carried out from the Terminal Control room at West Drayton, which very soon moves down to Swanwick.
With pressure on ATC to achieve max landing rates, CDAs, etc., and, in the case of Luton, to mix traffic with Stansted and handle the clockwork mice buzzing about, it's often very difficult to provide pilots with an ideal approach. Radar controllers know from experience what aircraft can achieve and don't think it's only you who gets popped on the LLZ above the GP. I was a Heathrow controller for 30+ years and I must have done it to thousands of flights. The flip side is.. if I had a quid for every pilot who has said "you can turn us in now" when they were 1000ft above the GP I'd be very rich! If you are in sequence of traffic and suddenly ask for more track distance it can severely mess things up.
Your penultimate sentence says a lot. Do PLEASE try and get a visit to West Drayton before they all move south. Sit with the radar controllers handling Luton and Stansted - see their problems and you might understand more.