This is just me, but I have no problem with Cochrane being Earth's first warpship pioneer, both as a "tinkerer" who somehow cobbled together a crude warpship for testing purposes (the Phoenix's first warp-flight) and as starting a whole new career as a result of all of the fallout from FIRST CONTACT. Cochrane founded the Warp Five Complex which apparently spearheaded Earth's technical strides in designing and developing new warp engines and starships. Perhaps the Valiant was one of those early international efforts to revive Earth's space program which eventually led to the Warp Five Complex being established. I prefer to assume that Earth built more than one of these early starships; perhaps in the 2060s-2070s, Earth began to experiment in building warp-propelled deep space vessels, probes (Friendship One) and test vehicles. No doubt some succeeded, some failed, and some "blew up on the launch pad". You can just hear either James Cromwell or Glenn Corbett's version of the character saying "Well, back to the drawing board we go, folks!" Either one works for me.
The whole theme of FIRST CONTACT (and of "Metamorphosis", for that matter) was that Earth (and Cochrane in particular) were repeatedly rejuvenated by embarking on endeavors in space travel and technological "tinkering". The TOS/Corbett take on Cochrane left me with the impression that when he discovered "the space warp", it was like a “Mr. Watson, come here, I want to see you.” moment. Maybe statues and schools being erected in Cochrane's name and likeness were indicative of how a battered post-war Earth unified around his efforts, and how, like the Apollo moon missions and other great strides, this "valiant" effort helped to "show the way" for the human race to restore and rebuild itself. Riker, Troi, LaForge and their landing party did seem to tell Cochrane that the arrival of the Vulcans resulted in a kind of 50-year planetwide revolution of sorts, becoming a permanent Renaissance for the human race.