Anything is possible with enough money and political backing!
Whilst a single London Terminus might be the way things would be built if you started from a clean sheet, there are numerous issues with such an approach.
Firstly there's the question of space. Even if all the lines and platforms were bored deep under London (which would be a huge project in its own right), you would still need a massive station building at ground level to cater for the number of passengers. That would mean demolishing several blocks of prime real estate in central London.
Then there's the question of what you would do with the service patterns. By my calculations, there are 146 bay/terminus platforms across all the London Termini. The majority are close to their maximum utilisation. So to replicate the current situation, you would either need 146 platforms at this megastation - good luck finding space for that, even underground - or to join services up across the capital.
Now obviously the latter clearly isn't impossible - it is exactly what has happened with the likes of Thameslink and the East London Line, and what will soon happen on Crossrail.
But it does mean that you easily import disruption from one side of London to another, and that trains have to be suitable (both technically and in terms of their length and seating/door layout) for operation on both sides. There would be no opportunity for intercity services to have a longer turnaround to recover from possible delays. You would also have to have an unprecedented degree of grade separation.
Timetables would have to be completely rewritten and there may be some differences that are tricky to resolve (e.g. matching a 4tph service on one side of London to 6tph on the other side).
So there are lots of downsides and the question is - what real benefit is there? You can't possibly have a direct train from everywhere to everywhere. People would often still need to change trains if they were crossing London. The location of such a megastation could never suit all markets, so even for those heading to London, an onward connection might still be needed.
In short, it would be a gargantuan project which, given the Victorian railway legacy that exists today, simply doesn't make sense. In due course, there will probably be more links built across London - for example Crossrail 2. But they will likely all be of commuter-type services that can be segregated from other traffic.