My initial memories were from a flat that my parents occupied. I was very young at the time, and don't remember much. We then moved to a house (married quarters), where I lived for a year or so and made some friends. Then my parents decided that they could afford to buy a house, so we moved again. Some twenty years later, I had to assist with moving the last of the stuff out of that home because my parents had split up and the place needed to be sold. It broke my heart. For a few years after, I used to walk past the place, thinking about how one day I might once more live there. Then reality dawns. They cut down the tree in the corner of the garden, the old shed gets demolished. The old garage is still there, to my surprise, but where we buried our dog is concreted over as a driveway. The property has been modernised, and it's none of my business any more. The memories are still there, though. People have to move on for various reasons.
I do feel for the people who have to move out of properties that are in the way of such developments, and I believe that simply paying "fair market value" for a property is insufficient. Perhaps a premium should be paid on top to recognise the effort that the occupiers have put into making their houses a home over the years, but it shouldn't impede major developments that will ultimately benefit a far larger amount of people.
If it was my house that was being demolished for HS2, I'd be upset. It's no different from "slum tenements" being demolished in places like the Gorbals, for example, in the name of improving conditions for the local population.