Even if you mentally substitute the scant in-game dialogue with an absolutely gangbusters speech, the game still ends with a random postal worker demanding two major armies leave, and both commanders aquiescing and withdrawing their forces from the entire region.
It's a bit silly that you can talk the Master down so quickly too but at least Fo1 generally treats the player as an embattled traveler who's just passing through and who most people don't care about, rather than the messiah whose word must always be obeyed. The Master confrontation feels thematically appropriate too and like a narratively satisfying conclusion to the game's wider themes - the Master was a well-intentioned scientist who believed he was building a more resilient future safe from the horrors of the post-nuclear world and that the ends justified the means, one of the humans he sought to transform or subjugate came to him and showed him he was wrong, he realised with utter horror that all he'd done had been for nothing and that there was no way to justify himself anymore, the last remnants of his humanity came rushing back to him, tragic suicide etc etc etc.
The game still ends with you selecting a few dialogue options but at least you can kind of see the overall shape of what that conversation was about and it forms an appropriate conclusion to the game's story, which takes a little bit of the lameness of clicking to win out (and obviously you also have to get the evidence and choose the option yourself rather than having it tagged for you).
Meanwhile the Lanius and especially Oliver conversations don't really connect to any themes in the game as far as I can imagine. It's not like New Vegas was a story about logistics and supply routes that makes the Barter solution feel like a beautiful poetic coup de grace to the plot. The conversations are just there because Obisdian recognised that people would expect/demand a speech solution to the finale. If New Vegas has any overarching theme, it's the dangers of nostalgia and repeating the mistakes of the past (as Avellone relentlessly drills into your head in Lonesome fucking pissing shitting Road), but the conversations with Oliver and Lanius don't really touch on that as far as I remember.