A new alignment into central Liverpool would not be straightforward from an engineering point of view but where there's a will there's a way, as is evidently the case with Birmingham, Manchester & Leeds. I've looked into this quite a bit and really, there's only two sensible locations for a city centre station - Lime Street and the old Exchange site (Moorfields essentially), as mentioned by HSTEd. Any new line would have to arrive at one of those two locations, in my opinion.
As for relatively low rail traffic compared to Manchester, a lot of this will be because of the low frequency, rather than the low frequency being a result of low demand. Whilst Liverpool has about half of Manchester's demand to London, it has only a third of Manchester's service. Also, Liverpool's the only core city to have a London frequency of less than 2tph. The problem with this low frequency is that it causes what I can only describe as 'seepage'; essentially, those who would naturally use Lime Street end up using other stations because it works out quicker than waiting for the next Lime Street service. In fact, there's no station where National Rail Enquiries doesn't give another station as an option for London. Even Lime Street itself, half the time, it is recommended to get a train to Crewe and change. Manchester and Chester trains call at Crewe and so people who would naturally be in the Liverpool rail market are supporting Manchester and Chester services. Lime Street's near enough unique for a big city station in this regards. Stick Manchester Piccadilly, Leeds, Sheffield etc to London in National Rail Enquiries and they don't suggest changing at another location ever.
Liverpool not being given a captive spur has little really to do with serving Runcorn, Crewe and Stafford. At the end of the day, Stockport, Macclesfield and Stoke haven't stopped a Manchester spur. It's not even cost. If they wanted a Liverpool spur on principle, they'd ensure to justify it. The real reason is lack of paths. Remember, Network Rail's own proposals called for a West Coast high speed that included a captive spur to Liverpool, as did the Greengauge21 proposals. Whitehall, however, wanted to serve its Yorkshire & The Humber (Leeds) regional capital as well as its North West one (Manchester), so the Y-shape was insisted upon, along with Heathrow. Liverpool was the sacrifice.
And this is Liverpool's problem. It's by far the largest city that's been lumped into one of these regions of which it's not the considered the capital. So, Liverpool's an "intermediate destination" as HS2 Ltd call it, considered more akin to Crewe, Stafford etc than Manchester or Leeds. It's the sad consequence of an overly centralized state (surely the most centralized large country in the Western world) and one that will eventually kill Liverpool if it is not replaced with a better way of doing things.
