If everything had gone to plan, the alien would have been purged, the Human Webway completed, and then the Navigators (presumably) killed off. That might lead to another purge of mutants and even psykers. As much as the Emperor felt denying Chaos's existence was the best way to deal with it, he would at some point have to face it.

With aliens wiped out and mutations either also wiped out or controlled, the only remaining threats are Necrons, Chaos, Orks, any potential civil wars, and the eventual arrival of the Tyranids.

If no Heresy-level events (ever) happened, then no civil war, in a galaxy where the Legions are loyal and the Emperor is mobile, are ever going to last very long.

Necrons may not be classifiable as a separate threat from aliens, and without a mass awakening like we get in 40,000, they may actually be easy(-ier) pickings for the Legions.

Orks are essentially unbeatable, but a new, greenskin-focussed Crusade might be called, to take their numbers down and begin managing them. Maybe the Emperor and Mars figure out a way to wipe them out.

With the Human Webway completed, the Astronomicon is shut off, and the Tyranids no longer have anything lighting up the Milky Way (if that is even what attracted them.) Even if they DO still arrive, they'll be arriving at a galaxy with 10,000 more years of the Emperor's guidance, and Dorn and Perturabo's fortifications. Plus Legions. If they came all at once, it would be a problem. But the Hive Fleets we've currently seen probably wouldn't be.

Which leaves Chaos.

The Eldar's extinction could weaken Slaanesh, in theory. And with the Webway completed the Emperor would undoubtedly have moved on to other projects, and I can't imagine "killing the Chaos Gods" wouldn't be on that list.