The problem is the word 'essentially'. Four cities: London, Birmingham, Manchester and Leeds are on dead ends. That is not giving them or the rest of the cities a service. Why does it make perfect sense to create radial routes into Birmingham, particularly when they don't join up with New Street? I just cannot see the Swiss, Germans or Dutch proposing something so stupid.
Because these dead-ends do make sense when you see the way that passengers actually flow around the rail network. There is no fundamental need for trains heading into Birmingham to then continue out again. The only other large cities where they could head will have their own dedicated HS2 service involving no time-consuming diversion through the city. The places that won't have their own service are then for the most part too small for it to be worth sending a multi-million pound 360km/h trainset trundling along a commuter or regional line to visit.
Look at the way that the British rail network works today and you can see pretty well why HS2 will follow effectively the same model. While it is often possible for trains to continue beyond their normal terminus this is relatively rare, or they do so to visit significant areas that justify a service. Virgin Trains West Coast services to Manchester run to Piccadilly and then terminate, while they bypass Birmingham completely by running along the Trent Valley. After Rugby, VTWC trains either head up directly to Birmingham, Liverpool, Manchester or Preston/Carlisle/Scotland.
The trains that do run through these large city centre stations are the CrossCountry services, which exist for the sake of inter-regional connectivity. However, as a result of that they have to be very slow, stopping much more frequently than their counterparts going to/from London. There's no way of making them faster without disrupting other regional services and connectivity. HS2 will address some CrossCountry journey types but it can only efficiently do so by bypassing as much of the existing line as they can. Running a Curzon Street-Manchester on HS2 means missing out quite a few stations, but that means having a much faster end-to-end journey time that is actually worthy of the cities that it serves. Meanwhile, the current path is still available for those needing to connect to intermediate places like Wolverhampton. If HS2 trains are to run through Birmingham I can really only see that happening with a new dedicated line, but that line would only be justified for trains heading south-west where direct services wouldn't otherwise be possible. However, that would add a significant amount of cost and difficulty onto the project without really improving the services that are actually justifying the construction of the line in the first place.
A set of lines from Brent Cross or anywhere else does not make a network. That's the problem with guessing.
The arguments you were making are highly reminiscent of the High Speed UK 'proposals' which included just such a Brent Cross Interchange.
