This is where you have to remember that GRRM, despite his meticulous 'world-building' and generally quite realistic approach, is a fantasy author...
The idea that a war which took place 2,000 years before the events of ASOIAF (according to the AWOIAF entry), was prosecuted by the Arryns of the Vale, and that they were a dominant house then and still a dominant house 2,000 years later, is obviously bananas in human historical terms...
I don't think there's a single royal house or noble dynasty in the history of the world anywhere that's lasted for more than two or three hundred years at most.
The notion that the same ruling family has managed to remain reproductively intact, never mind militarily and politically dominant, for 2,000 years... And that the broadly medieval setting of that world has remained largely unchanged across such an enormous timespan... Well, it reminds us that this is just a fairy story after all
That's very true, and I kind of wish he didn't have such huge timespans in places! What I REALLY like is how the whole history of the Targaryen dynasty on Westeros just goes back under 300 years. Seems very plausible. But anything before that, and suddenly we are talking about ridiculous spans of time.
And the Arryns are an Andal house, not among the first people to set foot on Westeros! The Starks and other 'old god' houses are descended from the First Men, and their lines go back even further!
The way I like to see it is all as myth.... Perhaps there wasn't much good or precise record-keeping 'back in the day'. Perhaps this War Across The Water actually happened 500 years ago, and went on for 50 years. But with lack of decent record keeping it has developed over the generations into something of a legend.
Well, that's what I'm telling myself!