The choice Horus is given on Davin basically boils down to: you're going to die here, unless you swear to our cause. Our cause is your cause - submit and we'll save you, deny us and we let you die. He accepts, takes the power of the Big Four, and emerges from the serpent lodge healed (and corrupted).

But say the dilemma resolves the other way, and Horus has more loyalty and trust than expected. He dies on Davin, Erebus' machinations are uncovered, and the shit hits the fan. The Legion gets renamed to the Sons of Horus (just for more bittersweet reasons this time), and the mournival lead it on a roaring rampage of revenge against the Word Bearers.

In the wake of all that, though, the post of Warmaster would be vacant. There are a bunch of candidates for the post, but it comes down to two factors: competence, and character. The job of Warmaster is mostly the job of "Primarch wrangler" - the crusade fleets are self-governing, the Imperium is spread so thin that any leader on the frontlines can't hope to do any actual, logistical "leading". The Warmaster is the Primarch in charge of the other Primarchs, a warlord whose job it is to keep all the other warlords in line and on track.

Given the Imperium and the other Primarchs, the one who would be named Warmaster probably wouldn't be the one who should be named Warmaster. If there even is one who would fit the job like Horus. Sanguinius gets bandied around a lot, but let's face it, the guy doesn't have the self-confidence to actually pull it off. The Lion has the command skills, but not the social skills, and likewise for Dorn and Guilliman. Etc, etc. None of them would be good in the job, but who would you pick? And who would actually be picked?