If it was in the UK it would have Grade 1 listed building status at the very least, and anyone just tearing into a national monument like that with a digger, because they imagined they were the tyrant king and didn't need anyone's agreement, would be in court before their feet touched the ground.
I mean, I recognise that anyone British has a bit of a cheek disapproving of someone damaging the White House but <shrug> I'm surprised if a president can just decide to do that on his own whim, when he publicly stated he wouldn't touch the existing structure of the building.