I just think that this is a horrific decision, but it is somewhat understandable having seen the letter, and it is completely true that lines with basic hourly trains in Southampton (or indeed the whole solent area for that matter) really have had little success compared to other cities, and its a sympton of the relatively awkward network in Southampton where nearly all traffic has to be consolidated into one 4-track station (Although I know it would have become 5-track had this plan ever worked out), a station not as centrally located as others, and with no real alternative.
Compared to other cities, although there are clearly local lines, they have been given very little love, and it just leaves smaller stations to miss out while all of the money is thrown at the fast trains if they can fit in local stopping services. Even Totton now misses out on having little more than hourly trains to Winchester or from Southampton, so it gives many places in the Solent little incentive to use the poor rail services as they are, and you get stations like Redbridge and Millbrook built-up areas only getting less than 30,000 passengers annually with hourly services to Romsey and Salisbury. If there were frequent all-day connections to London Waterloo, as there were from many stations before COVID, that offers a service that you can't easily do by car, and thus gives some incentive to use the service.
To make the line a success in my opinion, you would have needed at least a half-hourly service, journey times comparable or faster than by car, and maybe some through trains beyond Southampton, and that was obviously never going to happen with budget cuts to railways, even if the business case came out only just positively enough for them to proceed
Now that the decision has been taken to scrap this project, is there any possibility that one of the future steps to the line is to lift some of the track, given there are only 3-4 services a day that only run as far as Marchwood. Given that there is now no credible case for improving the line, it could just be downgraded to save Network Rail some costs on a line that they will likely see with having little future?