The nationalist politician is successfully conflating three very different things here.
There's certainly an argument that different parts of the UK are under/over-represented by Barnett Formula decisions, something that becomes a lot harder to assess when deciding which things are "UK" projects (and therefore Barnett doesn't come into it). Problem is, this is a Grass Is Always Greener kind of debate, it's easy to see the things that they get in other regions/areas and be envious without appreciating that these things often come at the price of other things - e.g. prescription charges - I don't think we'll ever assuage people's concerns about this - even if you rip up the current UK and create a fully federal utopian structure you'll get nationalists keen to point out some discrepancy or other. Many other threads see the complaint that "if this small town were in Scotland/Wales then it'd have had it's railway reinstated ages ago because these Celtic countries are much more progressive", so it's interesting to see the argument here along the lines of "if Lampeter were in England then it'd have had it's railway reinstated ages ago because England would find the money". Grass is always greener
Secondly, there's the pure politics of the fact that a service from Holyhead to Cardiff has to go through England... does this really bother people? I have colleagues who commute from Halfway into Sheffield City Centre without worrying that their Supertram left Yorkshire and ran through The Midlands for part of it's journey, without worrying about it. Maybe that is a big issue if you're Welsh, but I find it hard to get particularly upset about.
Then lastly, even if you decide that Wales can have a billion pounds (because it's easy to misunderstand the DUP situation and the fact that Northern Ireland may have some fairly significant reasons for lack of public investment over the past generation, if you know nothing about the place)... is Carmarthen to Aberystwyth really the best place for it to be spent? Okay, it's seven hours between them at the moment but then few people would be daft enough to try such a journey by train - it's a long way from Rhymney to Merthyr Tydfil by train (compared to as the crow flies) and I don't see anyone insisting that we build a direct link there. What would be the demand? Normally, new lines work because you have a big city at one end (Edinburgh, Cardiff) and an economically deprived town at the other end (Galashiels, Ebbw Vale), so it's obvious what the service is targeting - people commenting into the big city, people unable to get jobs in the town, people unable to afford houses in the city and therefore looking at moving to somewhere cheaper. Simple.
But (ignoring the nice shape it makes with a crayon on your map), what's the main demand for a line in rural Wales? Are there large numbers of people in Carmarthen unable to find jobs in Swansea who are eager to commute to the booming metropolis of Aberystwyth? Or do people really think that there will be significant numbers of people in Aberystwyth willing to take the train for over two hours/ over a hundred miles to commute in Cardiff? I can see it being handy half a dozen weekends a year when the Students are arriving/leaving but what about the rest of the year?
Essentially, I can see the logic in the first point, I can see why you could look at HS2 and decide that "if there's money for that then there should be money spent in my back yard", I get that. It's a powerful starting point for an argument. Throw in some envious reference to the DUP and it's easy to believe that Wales is hard done by as far as infrastructure goes.
I'm unmoved by the "lack of internal north-south line", but I can see why it might play well to a certain demographic.
But, even if you buy the first two arguments, it's thin gruel to accept the idea of Carmarthen - Aberystwyth being what to spend a big pot of money on. I can see the attraction of hoovering up some 75mph DMUs and throwing them at a proper clock face service from Swansea to Milford Haven/ Pembroke - there's certainly an argument that these fringes lack a good enough service. But there are surely a lot of other better projects to spend Welsh money on - removing single track bottlenecks, trying to give Cwmbran a proper service into Newport/Cardiff (something equivalent to a Valley Lines frequency, instead of being dependent upon unreliable long distance services), more double track north of Wrexham, extending the wires west of Cardiff, using the TramTrain functionalities to expand Valley Lines services beyond their current termini. It's not like there's a shortage of things that the money could be spent on - I guess that it's more a case of politicians knowing that suggesting an Aberystwyth - Carmarthen line every few months plays well with the kind of nostalgists who like the idea of investing in rural areas, with a handy dose of nationalism (even if heavy rail is over the top for that kind of route, where the largest unserved town has fewer than three thousand people!).
Great politics, terrible business case. Spend the money on something better.