Agreed, but using power to persuade that way gets easier the more power you amass. The most interesting story to tell in 2951, I think, woudl be where Suaron is just getting a foothold among the Haradrim and is beginning to consolidate that power, but isn't obviously the dominant force yet. It doesn't even need to be obvious to everyone, as it will become, that Sauron is the one calling the shots and pulling the strings.
I think there is a difference between the men of 2951 and the men of LotR. In LotR, the Haradrim follow Sauron because they have to. He has been dominating the region for decades, all the leaders are in thrall to him, and when he/they orders people into battle they have to go, even if they do it grudgingly. And by that time they might not be grudging; they have had 70 years (~ 3generations) to get used to the idea of beign led by Sauron's lieutenants and fighting with Orcs, and there are lots of inducements (tales of glory in battle, promises of plunder in the rich treasuries of Gondor) that will motivate some of them. They don't have to buy into or even understand Sauron's vision of world domination to fight willingly for him. And those who are visibly unwilling probably won't last too long.
In 2951, on the other hand, we can (if we choose) portray a society that, while traditionally hostile to Gondor, is not thoroughly dominated by Sauron. Different people may have different motivations for which side they choose, but I don't think any of the Haradrim at this point could be considered enslaved (int hat they have no choice but to obey). That will come in time.
Yes, as we move toward LotR time and more and more of teh Haradrim unite under Sauron they will be able to annihilate anyone who doesn't go along with them. But I don't think that should be the situation in our frame story. If Sauron just takes over and immediately wields crushing military force in Harad our story won't be that interesting.