please empty your brain below

Why ineffectual? It means that Melton and Oakham get a direct train to and from London every morning and every evening. There are much larger towns in the East Midlands that can only dream of such a bounty.
It's noticeably quicker for passengers from Melton Mowbray and Oakham to catch a non-direct train, via Leicester or Peterborough, than to catch the Ineffectual Train.

In contrast, the other three trains across the viaduct don't wait in stations for 30 minutes.
Indeed, but a direct train is attractive to a significant number of passengers, especially given the failure of most TOCs to honour advertised connections these days.
The train I sat on for three hours spent 25% of its journey time stopped in stations going nowhere. The directness wasn't especially attractive, as low passengers numbers confirmed.
"Go catch that one, pleads the guard"

To which your response should have been "certainly, could you please just endorse my ticket so that it is valid for that train?"
In the extended version of what the guard actually said, he made it clear that switching to the other train was an option available only to holders of certain tickets, and that those with specific bookings would have to stay put, but I merely hinted at this level of detail in the next sentence of my abridged narrative. Sorry.
I wonder why the line over the viaduct wasn't singled despite only 4 trains per day utilise it.

Possibility No 1.

In the extended version of the narrative the reference would be to 4 passenger trains per day. I think this is the likely reason.

Possibility No. 2.

Singling a railway costs money to do and doesn't make sense unless it is a suitable time to do it e.g. resignalling to be done anyway or rails need replacing. Less likely but the Bromley North branch is still double track except at Grove Park station despite only having one train at a time normally.
The table under the abridged narrative specifically mentions four passenger trains a day.

I could watertighten every post I write, but that'd be tedious rather than pedantic.
A train which I'm going to describe as Ineffectual, but which you might attribute with a different adjective, is scheduled to depart Derby station for London St Pancras International station each weekday at 16:36 (certain bank holidays and days with engineering works excepted). Before this train departs, staff at Derby station and aboard the train undertake announcements suggesting that passengers should not catch this train if they are heading to London using Anytime or certain other open tickets. Instead they recommend waiting for the scheduled 17:01 departure which is scheduled to arrive into London St Pancras International fifty minutes earlier (and yesterday arrived fifty-two minutes earlier). Even the train following the 17:01, namely the 17:23 from Derby, is scheduled to arrive at London St Pancras International twenty minutes before the 16:36. This so-called Ineffectual Train is scheduled to take two hours and fifty minutes to reach London St Pancras International, whereas trains following a more direct route can be scheduled to reach the same terminus in only one hour and twenty-eight minutes (and yesterday arrived early so took only one hour twenty-seven). But I chose to book my passage on the 16:36 from Derby using the Megatrain option on Stagecoach's Megabus website, because the fare is relatively cheap in comparison to the high fares otherwise charged by East Midlands Trains which generally exceed £30, and cost £63.50 if purchased on the day. By buying several weeks in advance I was able to ride all 144.9 miles from Derby to London St Pancras International for £6 plus a 50p booking fee. I also chose this particular service because it crosses what has been described elsewhere as Britain's longest masonry viaduct, an infrastructure feature which is scheduled to be crossed by only four passenger trains a day (and not at all at weekends or on bank holidays unless engineering works or some unscheduled diversion takes place). This viaduct is one of the finest sights partially in Rutland and partially in Northamptonshire.
So why does it run then? It's not a "parliamentary" service (run in order to avoid the formal closure procedure), as the line went through that process in 1967 - the present service was only launched in 2009.
The through service which launched in 2009 was one morning peak train from Melton Mowbray and one evening peak train back from London.

"This new link will provide many opportunities for passengers from Melton: it will serve travellers who need to arrive in London in time for a morning business meeting, and leisure travellers who want to enjoy a full day seeing the sights of London."

The Ineffectual Train is a later addition.
So no posting from Matlock then....
East Midlands Parkway? Even if it's not near any significant centre of population, couldn't they at least tell us what county it is in?

dg writes: That wouldn't be terribly useful. Although it's in Nottinghamshire, it's only 300m from Leicestershire and 1km from Derbyshire.
20 minutes in Derby. The incredibly slow train home. I'm presuming you didn't go up there just to do this particular train journey?

Or did you... Well, I wouldn't put it past you.
My chosen train when returning from a visit to family living near Derby. And usually a carriage to myself when crossing afforementioned viaduct. Lovely.
'flat hills'. ho hum, you should maybe explore east Leics sometime, a rural backwater maybe, but tranquil, beautiful villages, big skies and hills you won't forget.
"The train I sat on for three hours spent 25% of its journey time stopped in stations going nowhere."

Pah that's nothing. On Saturday I travelled from Leeds to London. Left Leeds at 19:45. Arrived London Kings Cross at 03:30 on Sunday morning. I think we spent much longer on that train going nowhere....
Ah, the Witham, the Welland, the Nene and the (Great) Ouse. Rivers of my childhood. Also lived for some time near the Trent, close to Ratcliffe-on-Soar; it was the marker that we were nearly home.
The Ineffectual Train runs to London for the last time today.

From Monday 21st May 2018 it terminates at Kettering, and is timetabled to miss a connection to London by one minute.

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