I think there may be a number of issues that cause the lack of support:
1 - the benefits have not been explained. It is sold as faster trains to London, rather than more capacity for trains on the existing lines.
2 - if the benefits were explained, it will look like another South East centric scheme - i.e. it's for London commuters mainly - any speed benefit is a by-product, not the main point.
Unfortunately now that Rishi Sunak has cancelled Phase 2A and 2B it does look a SE Centric scheme, but it wasn't previously. Capacity released by HS2 full scheme applied to ECML, MML and WCML with respect to Intercity services to / from London and to XC Intercity services between Birmingham and York. It would also allow for capacity around stations to be provided on a more local basis eg Milton Keynes to Birmingham (or London). Or how about Tamworth to Derby, Sheffield or Birmingham?
3 - the benefits are offset from the costs. For GWR stations on Crossrail, you had the cost of the disruption from electrification, but also the benefit of modern (and for some stations, more frequent) trains to London. For HS2, the disruption cost is borne by people remote from the benefit - the Buckinghamshire/Northamptonshire villages are the ones living with the disruption of the build and ongoing operation, but will not benefit from additional capacity on their local line (Chiltern/Met)
But you could argue the same applied to HS1 for the populations of Tilbury and Rainham (Essex) where they took all the disruption of building a railway they themselves cannot use because it doesn't stop there. Indeed HS1 was routed this way because the residents of the Garden of England did not want HS1 spoiling their view of it (mainly Tory). Now of course the richer people are complaining about HS2 because it passes through their green and pleasant land but they cannot use it. Swings and Roundabouts for me, I'm afraid I have no sympathy with the HS2 complainants and their case which has not been helped by their MP Greg Smith who has done nothing but complain about HS2.
3a - where existing rail lines are affected (mainly Old Oak Common), the people affected have had a lot of disruption already with the Reading rebuild and then electrification - now they are having their journeys slowed down for interchange with and (if Euston is not build) crammed with people from HS2.
The disruption could be managed. Euston is one example of this where the GWR services have been diverted. Could more services have been provided this way? Waterloo as per previous occasions has not been used this time, should some services have been diverted via this route?
In terms of post construction I don't think most Intercity passengers will see loadings increase from OOC into London and vice versa. If anything people will get off GWR services and head to either Elizabeth Line services or Euston or leave OOC station altogether.
The biggest challenge will be on Elizabeth line services with the western services seemingly full at certain times of the day so most of these people will be using services starting / finishing at OOC which will only have six of these off peak and 14 at peak based on the current timetable. The Off Peak looks challenging based on the current WTT.
4 - people are suspicious about the actual benefits of the line - will it be cheaper for people to travel, or will they be forced into paying a High Speed Premium - this is especially true of Manchester if (as the Wikipedia article suggests) there are 3tph, would this be at the expense of the existing services?
I hope the DfT will not set a premium like they did with HS1. if they want modal shift but whether it thinks that way who knows.
However we are getting to the point where the WCML is full then the DfT may well put the prices up anyway to stifle demand or use it as a means of (at least) part funding HS2 construction or its overspends as the DfT sees it.
