Electrification would be quite akward in North Wales I think. The Llandudno - Manchester wouldn't be able to use electrification if it was only between Chester and Manchester (unless bi-modes are built for the job). If you wire west of Chester at all, I think you need to go all the way to Holyhead and do the Blaenau Festiniog branch otherwise there will be an awkard diesel island (unless you build a new line from Bangor to Porthmadog). Blaenau Festiniog's a problem in terms of micro-fleets anyway though I suppose. You also have the 175s that are based at Chester. If north Wales was wired they would only be used on MAN-CDF/SWA and Chester-Cardiff services, which would allow much-needed longer trains on MAN-CDF/SWA but might still leave some surplus units.
The Welsh Government have been going completely the wrong way about the Holyhead - Cardiff service if you ask me. They had the right idea with the original Y Gerallt Gymro I think, just 7 (I seem to recall) intermediate stops between Holyhead and Cardiff and an exception to the standard pattern, rather than a frequent service. It ought to be 2-3 such express trains each way per day, and a change of train required at other times.
There is frequent talk of a new hourly TP service from Chester to Yorkshire after Northern Hub, probably fast.
ATW would probably like to run 2tph but they haven't the stock and the decision about where to start it (Chester, Wrexham, Rhyl, Llandudno Jn) would take years to resolve.
The line is on the short list for early electrification (as is Crewe-Chester), but that is only likely to generate split services at Chester.
Chester-Euston (and Birmingham via Stafford, the proper route

) could go electric.
What route would the TPE service take between Chester and Manchester? The franchise consultation seemed to suggest everything on TPE would run either to Manchester Airport or Liverpool, Chester doesn't seem to fit with either of those. You have a similar question too about whether it should continue to Llandundo, Bangor or Wrexham rather than terminating in Chester.
I agree about having Chester to Birmingham trains via Crewe and Stafford. That's one reason why the planned HS2 terminus in Birmingham is such a missed opertunity. If,
as I propose, there was a tunnel mouth at the north end of the station (like Stratford International, maybe), HS2 trains could reach Chester. Then, the hourly Euston-Chester/Holyhead and Birmingham-Chester/Holyhead links could be catered for by a single hourly service instead of two. On the north Wales coast, you could end up with something like:
- 1tph Holyhead - Chester - Crewe - Birmingham (HS2) - Euston (fast)
- 1tph Llandudno - Manchester (similar to today)
- 1tph Bangor (Holyhead every 2hrs) - Llandudno (all stops)
- 3 trains per day Holyhead - Cardiff (express)
1. I think there are some people in Wales who would like to see some of the Birmingham/Shrewsbury - Wrexham - Chester services extended to Liverpool via Halton curve. For providing an improved access between Wrexham & Liverpool, that would certainly be a lot cheaper than electrifying Wrexham to Bidston.
Or use electro-diesels (eg. upgraded class 73s) via one of the existing routes, provided Merseyrail will let you have a path. With regard to the above point about direct Chester-Birmingham services too, I think the current Birmingham - Holyheads should be reduced to Birmingham - Wrexham, terminating in the bays used by Wrexham and Shropshire (to save them traversing the single track bottleneck between Wrexham and Chester).
The a Welsh Government has an aspiration for an hourly Cardiff to Holyhead service this has been discussed many times on this forum. I am in the camp that says this service would undermine the prospects for the north wales coast being electrified.
Even the current every 2hrs Holyhead-CDF is too much for north Wales electrification. The Holyhead-Birmingham also stands in the way of north Wales wires. Everything from north Wales needs to go to Crewe/MAN otherwise the marches line will need wiring too.
The Halton Curve... dunno. If you are going to spend money on it then it needs to have at least one train an hour, but it'd be a lot of money to spend just to give a further Liverpool - Chester service (considering the four direct services each hour). If it's to give Liverpool - North Wales a direct service then that sounds like more justification, but the current service frequency along the coast is pretty decent already - would a Liverpool service come at the expense of a Manchester/ Birmingham/ Cardiff service?
A Liverpool - Halton Curve - Chester - Wrexham - Shrewsbury - Hereford - Newport - Cardiff service every hour (or maybe bi-hourly, with a Liverpool Halton Curve - Chester - Wrexham - Shrewsbury - Wolverhampton - Birmingham service dovetailing) would be an ideal way of linking places whilst improving the case for North Wales Coast electrification.
Liverpool-Chester-North Wales would require wiring the Halton Curve too, otherwise it causes the same problem as too many Cardiff-Holyhead trains. Liverpool-Chester-Wrexham-Shrewsbury therefore makes more sense, maybe continuing to Cardiff (or maybe alternately to Cardiff and Bristol). I don't see any point in taking up paths on the single track between Chester and Wrexham with Birmingham services, especially since Wrexham should be able to have through trains to Birmingham without them running through to Chester.