It would be disastrous for HS2 to terminate permanently at OOC. If money is tight, proposing that HS2b would still be built from Crewe to Manchester, even if the Euston-OOC is shelved, is very short-sighted; only a handful of HS2 trains per hour are proposed to serve the segment north of Crewe. It would adversely affect very many more potential passengers and significantly downgrade HS2's usefulness, potentially jeopardising the overall success of the whole HS2 project, and its primary aim of improving connectivity from London to the West Midlands and to North-West England.
The current published journey time from Euston to Birmingham by fast trains is 76 minutes compared to 45 minutes by the planned HS2 service. The planned HS2 journey time from OOC to Birmingham is 38 minutes. However, one would need to add 25-30 minutes to travel from central London (say Tottenham Court Road) to OOC and then change trains and transfer to the HS2 train, making the overall journey time from central London to Birmingham about 63-68 minutes, which is not a significant saving over the current journey time of 76 minutes.
If HS2 is permanently curtailed to Old Oak Common, then people from Birmingham, Manchester and other destinations won't use it.
I live on the Western outskirts of Birmingham, and currently if I want to take the train to London I get a bus and then the tram from Edgbaston Village, alighting at New Street station. With HS2, it would be a further 10 minutes on the tram to Curzon Street.
I would not be inclined to go past a station that has direct trains to the centre of London, in order to go to another station that doesn't have direct trains to the centre of London, particularly if, as I suspect, fares on HS2 are substantially higher.
The other thing about Birmingham Curzon Street is that you can see the site of the station from the existing line from London as it approaches Birmingham New Street. It would be somewhat ironic if you were to stand in a brand new station waiting for your train to the outskirts of London, watching trains go by that are going to, er, the centre of London.
I think would be even worse at Manchester Piccadilly. Why would anyone want to get a train to Old Oak Common when there are direct trains to Euston every 20 minutes?
Some people say that the Elizabeth Line at Old Oak Common would be convenient for onward travel to destinations in Central London. Whilst that may be the case, we already have a thread on these forums saying that Elizabeth Line trains are busy at peak times. I don't think people from stations in between Reading and Paddington, plus those from Heathrow, are going to be pleased if hordes of people from Birmingham and Manchester are going to try and pile on to an already busy train at Old Oak Common.
Talking of the Elizabeth Line, I can remember when Crossrail (as it then was) was cancelled, because the recession of the early 1990s meant that the line was "..no longer needed..". Then subsequent economic growth meant that the tube could no longer cope, and the Elizabeth Line became more of a necessity.
Similarly with Docklands and Canary Wharf. The Docklands Light Railway was originally conceived as a cut price alternative to extending the Jubilee Line. The DLR soon became unable to cope with passenger numbers, and so the Jubilee Line extension had to be built, as well as the expansion and extension of the DLR.
So I believe that HS2 will eventually built all the way to Euston. If Sir Keir Starmer is the Prime Minister after the next election, as seems likely at the moment, he would be responsible for confirming a decision to cancel a major development project in his constituency.
What would then happen to the big hole in the ground at Euston? It could be sold off to developers, but who would want to build there if, in 20 years time, there is the risk that the government of the day says, er, we're going to extend HS2 to Euston so we need to knock your development down.