What I know:
Alert height is a result of probability calculations for Fail Operational Approach and Autoland systems.
Simply a mathematical result so that with the redundancy of systems of a particular type of airplane, during the period of time from the time of crossing this height to completing the approach and landing, the subsequent failures of required systems are exteemly remote probability (below a threshold probability value).
That is all.
Below this altitude techinically nothing changes in the plane, however some extra warning systems are armed (or should be already armed -for example AUTOLAND light on AIRBUS-) to alert the pilot for the odd cases which this extreemly remote probability is breached