If there have been ships capable of making the journey for that long, why hasn't anyone done it in the interim?
Why haven't Humans gone back to the moon in forty years? Politics, money, other priorities.
Even if you go with the "almost 200 years" reference instead of the "over," it would still have had to be launched only a decade or two after Cochrane's first flight, and probably wouldn't have been capable of much more than warp 1.
This assumes that the Valiant, or at least it's engines, were indigenous to Earth's technology and not simply purchased from outside. While we don't know the exact timing, aliens (not just Vulcans) did travel to Earth following the first warp flight.
Or the Valiant might have traveled outward initially with Cochrane style engines, and at some point up-graded with extra-terrestrial technology. They journeyed "upwards," stopping to explore, periodically acquiring new technologies, then moved on again. Spending years or decades to reach the barrier.
Just because a ship is crewed by Humans and is a Earth ship, doesn't necessarily mean it was built here. Just "flagged" from here.
One of the things (besides the Vulcans) that prevented the construction of a ship like the NX-01 for the better part of a century, might have been Starfleet's (and it's predecessors) insistence that the ship be built of indigenous Human technology, and not foreign imported hardware.
Politics and cultural pride.
The operators of the Valiant may have felt differently.