I guess the problem is that unlike Friedman, Kirk isn't an expert on all things
Valiant - which is why, when hearing her call letters in the far reaches of the galaxy, he has to dig up the pertinent information from a source. And it's that source that tells him that the ship "has been missing for over two centuries", the exact wording.
Why would that source mistakenly report the ship as "having been missing" before her launch or even her construction? (I guess the builders could have been a bit careless, but...)
OTOH, even if the ship were launched 200+ years before the episode as stated, but factually fell into a wormhole or whatnot only several decades into her mission, why would Kirk's source report her as missing since 200+ years rather than since the factual deviation from flight plan?
The one way to have a decades-long mission end in wormhole displacement is to have the
Valiant launch long before the discovery of warp drive. If she has sublight engines as good as Khan, she might be well outside Sol or its immediate neighborhood in 20-30 years. If she has better engines (supposedly introduced in 2018), all the better. The need to assume a wormhole-style anomaly within the limits of Sol system goes away, then. Although why we would wish for this to happen when we know such anomalies
are there, I don't know. Rather, we might blame every incident from "One Little Step" to TMP to "The Royale" to "Where No Man" and for all we care "The Changeling" on one and the same phenomenon - the VOY gravity ellipsis, mistaken for a black hole in the 1970s. This
is the lit forum, after all - the smaller the universe, the better, right?
Timo Saloniemi