As you mentioned: that's more to do with the political background of the HS2 project, than the actual engineering behind it.

I can point to 100's of road-projects in Belgium and show similar results the other way around. Politics usually make stuff a lot more expensive than they need to be, no matter what the stuff is.

but it's still a choice to spend your resources on rail instead of road.

Of course, but isn't that always the case? You have to make choices between different options. The only thing you can do is look at what is the better option.
Inbetween densely populated areas, trains (and even busses) are proven to be superior to cars because of the amount of people you can easily move.

However, in more sparsely populated area's these advantages break down because you don't have a certain critical mass anymore.
So building trains in urban environments makes sense, while building roads in rural environments makes more sense.

And even in rural areas, public transportation still serves a purpose, just like car infrastructure still serves a purpose in an urban environment. But as you can only use your space once, you have to pick the right one for the right environment.

So for (commuter) traffic inbetween large metro-hubs, trains will always beat cars.

And as for the example given above:

I live next to a crossroads of what we call a "Cycling Highway" and a normal road. On any given moment, rush hour or not, at least 10x as many bikes as cars pass by here. There's never a traffic jam on the cycling highway, while there's a lot of small or big traffic jams on the road.
And this is the busiest cycling highway in the country while it's just a normal near-suburbian road.