If a second high speed route were needed to make up for the inadequacy of HS2, and Euston is the only place for a station, where would the second one terminate?
That seems to be the point that HS2 Ltd are making. That they can't terminate more than 18 tph in London within the reasonable bounds of the available property.
We must get it right first time, not leave it to others to patch up some decades later.
I think their point is that the only options for the a second station other than Euston are:
(a) pick a site, knock down everything on it, build a station there, and then run a tunnel there from outside London.
(b) pick a site, knock down everything on it, dig a big hole, launch a TBM from there to a tunnel portal outside London, build a station entirely underground and then rebuild over the top.
That's going to be expensive - the platforms alone are 415m long and about 100m wide for 9 platforms. That's 40,000 sq m of central London property before you start - even if you do build it underground so you can build back on top when you've finished, you still have to buy the ground to sell it back again.
You're also going to need to go somewhere that has excellent connections.
Honestly, I'd be tempted to say Farringdon - at least it will be well-connected as the point where Thameslink crosses Crossrail. I suspect you could put the concourse alongside the existing station, and build the platforms underground; run 800m roughly NNE and there isn't too much that you couldn't get away with demolishing; you'd just have to get under Clerkenwell Road and St John Street. It would cost tens of billions - far more than any of the Euston plans - just for land acquisition. You might get much of that back ten years later when you've finished construction, but you'd still have to pay interest on the money you used to buy it all up.
So, if you have a problem that can only be solved by throwing an enormous amount of money at it, then you shelve it and hope something comes up in the intervening decades. Someone might come up with a cheaper way of doing major underground construction without clearing the land above (TBMs are fine for tunnelling, but not much use for opening up the sort of giant cavern that a station would need).