Why such a stupid place? Its no stupider or smarter than any other place if you think of it as a split of the North American plate sometime in the distant past.
Incorrect. Plate tectonics don't work that way. The way the plates are moving is pressing North America against the Pacific plate. If North America is where you show it, the same action that created the Rocky Mountains will seal it with a bridge like Baja California.
You can't have a gap there without splitting the top off the North American plate roughly 50 million years ago. Even then it would be hard because the motion of both the Asian and North American plates is going to be pushing the northern bit from the west and to the west, respectively. You'd probably need it to drift north to avoid the Rockies sealing your gap. Of course, if the new subcontinent (Arctica?) is much further north it will accumulate ice and world sea levels will drop - connecting up a variety of old landbridges and making the Hudson Gap route you posit trickier.