Anybody sane in office would build the same kind of thing (hardened command and control bunker) but somewhere else in the area.
The argument for the whitehouse location would be "in the event of a nuclear missile headed for DC with little to no time to move ... " the POTUS could be moved straight down and have access to all that is needed for digital control, etc.
The argument against would be that's the one location almost guarenteed to get a penetrating atomic or conventional warhead (if anywhere) and it'd be better to be anywhere else.
That said .. any bunker or data centre might well be some distance away .. and the project is build a fast transport tunnel from the complex already under that wing to a new deep bunker some reasonable distance away.
And maybe NSA knows some attack vectors that we do not. So even geographically close by might have risks involved.
throwfaraway135•57m ago