Personally I think if Liverpool is to have services using the Marches Line, it should have direct services to Cardiff
I totally agree that some consideration should be given to operating at Cardiff
I'd respectfully disagree.
Shrewsbury/ Hereford/ Cwmbran/ Abergavenny (etc) already have an almost half hourly service to Cardiff (hourly ex Manchester plus bi-hourly ex Holyhead plus "WAG Express"), but no Bristol service - now that everything has to go to Cardiff under the Wales & Borders franchise.
But you've got roughly 150,000 people on the Marches line with no direct service to a decent sized city - which might be enough people to fill a 158 or 175 from time to time. The same could be said of the north Wales coast having no direct service to the nearest big city (Liverpool).
Obviously the Wales & Borders franchise have enough problems with capacity on their existing Marches services, before we have the luxury of worrying about new services/ routes, but I'll enter into the spirit of the OP's post.
I've suggested a Bristol - Liverpool service before (on the basis that there would be some 158s coming free, before the current electrification woes). Running via Crewe instead of Wrexham, partly due to the single line issues on the Wrexham line, so I like the idea of this. It's not another "London" Open Access proposal, it doesn't require reopening of some closed line (assuming that the Halton upgrade will happen).
But, part of the strength is also a weakness (in today's fragmented railway). It's great that it doesn't fit neatly into an existing TOC (so isn't competing/ abstracting) but touching on SWT/ GWR/ W&B/ Merseyrail (and on England and Wales) means that it would struggle to find a champion arguing in favour of it.
I can see the argument for putting Liverpool back on the XC map. But the problem is that there are always going to be significantly more "Cross Country" services north of Birmingham (2x Liverpool, 1x "Scotland", 2x Manchester, 2x Newcastle, 2x Nottingham... compared to 2x South West and 2x Thames Valley) that would mean a zero sum game where any Liverpool service (via Birmingham to Bristol/ Reading etc) would be at the expense of somewhere else - clever clever suggestions about splitting/joining long distance services at New Street notwithstanding.
The Southampton section of the OP's suggestion - I'm less keen on - a bit of a "dog leg". If you are going to target the "Granny" market of passengers who'd prefer to sit on a direct train for six hours rather than change in central London for a much faster journey then
you might as well go the whole hog and suggest extending this "cross country" service back to start at Brighto... nah, maybe not!