Again, just personal opinion here. I always felt that the NX-01 was named "Enterprise" at the request of Zephram Cohrane as a tribute to the folks who helped out with the first warp flight.
And that in the "original" timeline it was the "Dauntless". This would "explain" it being missing from the "Enterprise" models in Picards ready room or the pictures we saw in "TMP".
A VERY interesting concept. I like it.