The majority of capacity problems are on such flows as Huddersfield to Leeds in the morning and return in the evening. Myself I have no issue standing for 18 minutes to get home. If you want a train service where no one stands up to travel to or from work then carry on dreaming.
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The primary issues are in the peaks mostly, where nearly everyone wants to travel on the same train at times, for example the 1709 from Leeds, the 1725 from Leeds and the 1740 from Leeds, all heading towards Huddersfield. No matter how many carriages you supply, the train will be full.
Try travelling down south in the peak and then complain about overcrowding on TPE.
With respect, I think you are seriously mistaken.
You are correct that short distance commuting such as Huddersfield - Dewsbury - Leeds, Warrington to Manchester and suchlike do pose a capacity problem. And I also agree that it would be unrealistic for every person doing those relatively short journeys to get a seat. Standing up for 18 minutes or so, would, as you say, be no different to The South where everyone likes to say has a far superior rail network.
But the real issue on TPE, as alluded to by other posters, is at a weekend and especially on Sundays. At these times a reduced level of service, lack of 6 car sets and huge numbers of longer distance leisure travellers such as hen parties, stag dos, sports fans, shoppers, students going to and from home and many others means that people are having to stand up - and in many cases wedged in like the central core of London Underground during the week - all the way from Liverpool to Leeds, or Newcastle to Leeds, Manchester to Sheffield / Doncaster, Hull to Leeds - all long journeys well in excess of the 18 minutes you say people should just accept. Should they also just accept and be happy to stand up and wedged in for 60 - 120 minutes?
Add in the fact that whenever engineering works affects weekend services the affected services are normally simply withdrawn, without any effort to increase capacity on the remaining services, making them even worse.
Travelling on Friday evenings and at weekends on TPE really is a most unpleasant experience - far worse than a short distance midweek commute.
It is also bad for business as the TPE business seems to rely a lot on leisure travel. Commuters, like in the South, are a relatively captive market and will always have to commute from Huddersfield to Leeds.
It is a problem certainly not unique to TPE - but it is one which affects them worse than many others. It seems the issue is widely ignored by TOC management (not just at TPE) but also more widely by the DfT who only ever seem bothered by midweek commuter crowding and not weekend leisure travellers.