Why is there only one train an hour? Every other major city (some considerably smaller than Liverpool) have at least two. Leicester has four!
As a couple have rightly suggested, politics has a lot to do with it. It's been a trend in the last 30/40 years to run down Liverpool and big up Manchester. The reasons are various and multi-tiered but the regionalising of England into 'regions' has a lot to do with it. Essentially, if you're not the designated capital of said region, there's not much down for you. So, in the North West, if you're not Manchester, forget it. That's where the regional government offices are and most British institutions follow their lead, from the BBC to the NHS. It's the same everwhere else in England. It's great to be Newcastle in the North East. Kinda sucks to be Sunderland though. You'd think Leeds was the only place in Yorkshire sometimes, the way the BBC and the likes go on. I mean, the government announced the Manchester-York electrification as Manchester-Leeds, because Leeds was better known apparently, I'm pretty sure York's world famous in a way Leeds just isn't, but it just goes to show how Whitehall looks at its empire and how its mind is focused on its adopted capitals in each area.
What makes Liverpool's situation even more accute is two-fold; firstly, it's comfortably the biggest non-regional capital in the country. This skewes its image and makes people (as is often evident on here) tend to think it's a lot smaller than it actually is. Indeed, it's bigger than most of the official regional capitals, be it Nottingham, Leeds, Bristol etc. The second aspect is the 'second city project' centred on Manchester (and Salford) that Labour tried to implement in their latter days in office. This will undermine Liverpool more than any other large city, due to geographical proximity, as well as already being subordinated to Manchester within the North West. This 'second city' project was Labour's final strategy to tackle the North-South divide. Their first stance, upon taking office in 1997 was to deny that the North-South divide existed. Then, they turned to regional assemblies, which were ahistorical and were not to actually have any significant powers inherited from the centre anyway. After hostile feedback in all regions, the assemblies idea was dropped and they decided that what the North needed to emulate the success of the South East was its own London, with Manchester being the nominated city. As this is a rail forum and not an economics forum, I'll not go into too much detail about how that model won't work either but I'll say this - putting BBC Breakfast in Salford Quays will do diddly squat to tackle the North-South divide.
So, getting onto the rail side of things (apologies for anyone who cares little for regional politics but believe me, it's very relevent to the issue the OP raised), it's hard to gauge demand for Liverpool-London trains without having some hard statistics at hand, but I will happily challenge any theory that suggests Manchester has three times the demand Liverpool does. It just doesn't seem credible to me. So, as far as I'm concerned, either Liverpool is under-served, Manchester is over-served, or both are factors. Again, myths have been, albeit quite innocently, perpetuated that Liverpool has no economy or business community. The fact people seem to genuinely believe this (as well as crap about no one in Liverpool being economically active anyway) is rather depressing. Most stats I see related to this tend to be loose predictions. 'By 2025, Manchester will have X demand to London', based on what, who knows? It seems to be a self-fulfilling prophecy that the places with larger demand currently will have even larger demand in the future. Personally, I feel that they fail to take into account the idea that giving an area a superior service will encourage people in that area to use it more often, as well as encourage investment in that area, helping the economy, thus, reinforcing demand and the economic case for improving it futher, as does predicting a certain area will grow more than another.
A second Liverpool train to London via Warrington might make sense, if Warrington justifies the demand more than Runcorn. Warrington only has 1tph itself, if I recall correctly.; surprising considering its location on the WCML. I know this is a semi-official plan for when HS2 arrives but is there no reason why a train can't go that way today? As for HS2, it's a big, potentially fatal landmine on the horizon. If it puts Manchester an hour closer to London than Liverpool, as has been suggested, it will kill the city.
As for taking one of the two trains per hour from Birmingham, that's not going to solve much. For one thing, the London Midland proposed service would be much slower than Virgin's. It'd be more convenient for accessing inbetween destinations but I feel it's not worth sacrificing 2tph to Birmingham for. In a typically British way, Liverpool is pretty much the only major city not on the CrossCountry network. Most XC lines are a core 2tph. Not being on this network limits Liverpool as a direct destination. Having a 2tph London Midland to Brimingham service, albeit on nicer electric trains, so Liverpool passengers can connect with the hub of the CrossCountry network, is the minimum compensation. Anything less would be unacceptable.
The Hooton idea is interesting. I'm sure Hooton as a mainline terminus would be very popular with a lot of the southern part of the Wirral. Can't see any mainline trains running on the Wirral Line though. Essentially, Merseyrail is an island metro system with little to do with the rest of the national rail network. The line between Hooton and Chester already stuggles with capacity constraints, which is why 2 of the 4tph on the Wirral Line don't stop at Capenhurst. Line speed and signal improvements might alleviate this but the only way I can see Virgin Trains at Hooton is if Merseyrail is pegged back to Hooton from Chester. One thing that would do is help the case for re-instating the Halton Curve as the alternative way to travel from Chester to Liverpool. However, to get up the Wirral, Chester passengers would now need to change, where they didn't used to. Also, what effect would it have on Bache and Capenhurst? Would a short stopper service to Chester be needed? I doubt it would manage 4tph though, which Bache passengers are now used to. Perhaps the Crewe-Chester ATW shuttle could be extended. All in all, the Hooton idea might create more problems than it solves. Also, it'd seem weird seeing a train at Euston with 'Hooton' written on it.