Geez, what a sh!tfight! All I tried to do was explain to someone what "SHEED" was, honest.
I unreservedly apologise to all and sundry that my figures weren't exact, and were sourced from memory, well away from an FMS or Jeppesen Chart.
I've never refused it, it doesn't scare me, I can cope with just a PAPI. But I've also experienced difficulties in seeing the runway on a hazy day with the sun low in the western sky. I've also expressed a preference for the GNSS when I felt that the conditions made that a better option. Sometimes approved, sometimes declined because of the "flow". I confess to not understanding when arriving from the SE, why a PORTS or WAREN Zulu STAR doesn't work for ATC.
As to how high above profile it is, in the jet that I fly, the altitude the aeroplane wants to cross SHEED
were the altitude constraint not there is either just under or just over 2100' (I don't remember the exact figure), so that's close to a '400' to 500' difference to the FMS profile. It's high enough that the very gentle autopilot will still give close to 1500'/minute ROD (not all the way to the ground) to regain the desired profile once past SHEED.
Finally, though I've no experience of other makes of FMS, I'd be most surprised if any FMS operating properly, put the aeroplane above 2500' at SHEED.