(it's very British to say "this is too good, can we have something cheap and nasty instead please?")
Quite a lot of the cost is the NIMBY appeasement mentioned upthread. Something like a quarter of the line will be in tunnels. Making a slower line wouldn't make that any cheaper.
The extension to Euston was supposed to have 11 platforms. Even the reduced scope now being implemented is 6 platforms, I believe. All 11 were required to handle the eastern leg of HS2 [providing bypass capacity for the East Coast Main Line out of King's Cross and the Midland Main Line out of St Pancras], and services to Scotland and Manchester [bypassing the West Coast Main Line from Euston's classic platforms].
> If they'd put in another standard rail line instead
That would be crazy. In order to be a viable line to go from Midlands to London and reduce capacity, it would have to be at the very, very minimum as fast as that line goes today. So you are going to build a high-speed line of some sort anyway.
And that means maybe you can be a bit more adaptive to the terrain, but that also leads to more distance and thus more kilometers of line that has to be build.
A huge amount of the cost is simply buying the land, building the tunnels and bridges, putting up the electricity wires and so on. All that you would have to do anyway.
So basically at the very minimum you would need to build a 200km/h line, and nobody serious would even consider that. A 250km/h is the only reasonable 'lets safe money choice'. Going to a 300-350km/h line is going to be more expensive, but likely only by a few %, maybe 10%. But you would lose a huge amount of the benefit, as tons of study show time is a massive important to use.
So if you actually take into account future income from the line, building it to a lower standard would have been insanely stupid.
> taken up much less space
This is just straight up factually wrong. If you want to save money by changing alignment, you need more space, not less.
> would have been much cheaper
As I pointed out, much is simply wrong here.
> would have caused less disruption
Building would have more disruption and overall there would be more disruption in general.
> would have had a clearer business case
The business case, would be much much worse.
The people making that argument somehow think that you could build some rural 160km/h rail line and still get 90% of the benefit. Yet somehow no country who analysis this beliefs this and pretty much every single rail expert in the world doesn't agree with it either.
So the question you have to ask yourself do you want to believe the designer of HS2, most experts in rail technology or a bunch of anti-infrastructure activists?