why? because the mobility of millions is more important than your emotional attachment to the house.

Even if you accept that principle -- and while it's not unreasonable, I can also see reasonable arguments against it -- where does this policy end?

Let's get an idea of scale here. The entire UK national rail network currently supports approximately 1.5 billion passenger journeys per year. If we make some plausible assumptions about regular commuters, then probably 5-10 million individuals benefit from travelling on the rail network's approximately 10,000 miles of track more than occasionally. In other words, when you're talking about the mobility of millions, you're not really talking about building a small part of transport infrastructure that affects the property of a few unfortunate people, you're talking about building the kind of infrastructure that supports a population of 60+ million and gets built over many decades.

Let's also consider the likely alternatives. Major projects like new rail don't just affect a few square metres of someone's land when they pass through. Again picking on the UK, just because we have lots of conveniently available data about the new HS2 proposal, the government is now safeguarding an area 60m either side of the proposed route (for the first stage) so strongly that you basically can't do anything in that zone in terms of planning permissions. Obviously in terms of noise and potential disruption to local infrastructure and local travel arrangements, the effects of a major high speed rail link go far more than 60m from the track. So this isn't the kind of project where a single person with a 3-bedroom house is going to be throwing the spanner in the works. It's the kind of thing where an entire rural community is probably under pressure, or within cities with dense accommodation, potentially hundreds of residents in a single building, multiplied out by several buildings. The alternatives that avoid these problems don't just put a slight kink in the proposed route, they probably adjust the route over several miles to go around the entire area, or they relocate the routes and stations within the city so the new path isn't so disruptive, and maybe adjust the local transport infrastructure around stations to support this.

So, your idea of the mobility of millions vs a bit of emotional attachment to a house is not really what we're likely to be talking about for any single infrastructure project. What about some numbers on a more realistic scale? Does the convenience of 10,000s of people having a station a little closer to their office in the centre of the city so they can save two minutes of walking to work every day outweigh the inconvenience to 100s or 1,000s of people whose homes must be destroyed to make way or whose communities are split down the middle by the new route? Does saving a minute or two on a cross-country journey lasting hours outweigh destroying an entire community whose rural settlement is in the way? These are the kinds of argument that compulsory purchase/eminent domain really tends to raise, and they aren't nearly as one-sided as your comment about the mobility of millions might suggest.