If I am catching any form of public transport then I allow 5 minutes minimum.I'm taking a train journey, not an intercontinental flight. Boarding - not arriving at the station but boarding -a train one minute before departure time is adequate. By WTT I assume that's rail staff timetables. If it has times earlier than public timetable times then something needs to be changed.
Not that I catch public transport very often, normally its when the Ferrari is in for a service or the ash tray emptying!
A lot of intermediate stations its 30 seconds dwell time.Incidentally, how much time is allowed at an intermediate station for a train stopping there? I believe that in most cases for small stations it's a minute which rather blows your "allow adequate time to catch a train" thesis out of the water.
It isn't open permanently because it would be uneconomical to man it full time and undesirable to have an entrance open to the station. In theory it is meant to be season ticket holders only but the number of people who use it and then enter the station still needing to buy a ticket is very high. It can't be left closed all the time because all the season ticket holders would kick up a huge fuss, as they do already when it's closed.