The word “Empire” was not so negatively meant over a hundred years ago in our world, and it appears in the G4 where the Crystal realm could call itself “empire”, “Crystal Empire”. Moreover, it had turned out that empires often served as a gathering point for different cultures and peoples into political entities. Twilight did not have to be the sole ruler as the “empire” will be a matter of mutual friendship and greater rapprochement between the various realms - politically an alliance, but culturally an empire, as Twilight will have power as a model for the whole world, as it is on her values this concentration of power rests on. The other heads of state will thus consult with her, come to her assistance and coordinate their policies with hers if both jurisdictions go into each other’s interests. More like a kind of feudal version of the UN in our world. Twilight will be as powerful and influential as the UN Secretary-General in our world, in other words on the acceptance of her friends and equals.
Thus, a global society with significantly lower potential for conflict could arise, and can exist for a very long time under a set of norms created and maintained in the basis of Twilight`s philosophy. In our own world, we had norms for mutual coexistence, but this is broken by American arrogance, Russian dishonesty (Putin makes Danu look like a Boy Scout) and Chinese Self-impotance.
In Equus, on the other hand, there are millennial norms between the rulers that are so stable that it could be a long time between conferences needed to adjust the world after harrowing periods like the Storm King`s conquest wars that were stopped in Canterlot. Here it appears that Cunabula, which was previously deeply isolated before Discord’s invasion, is the exception to the rule. So Twilight thus has solid ground under her own hooves when she wants a global common society, the invasion of Equestria had made her realize that the whole world had to be integrated into a community based on reciprocity, openness - and friendship. It was her first political goal in her career, as she started her friendship school to spread her ideals and establish contact with non-ponies.
So an empire in her name had to be established - without having power, but to assert itself as a power factor with insight around the world rather than living in isolation blind to potential threats from the outside. So when the alliance is created, she had reached an important goal that we noticed in the last episode of S9. As the center of this “empire” - and obviously also a condition of existence for maintaining alliances - Twilight will be unique in the three continents as a role model and an ideal. This is something even the most powerful can hardly achieve.
And this can be accepted by the other heads of state as Twilight in contrast to Celestia can be a supporter of local government also in her own realm. Celestia and Luna had started a centralization policy that ended with Canterlot being the Versailles of the Equus. What Twilight wants is not to interfere in other people’s domains in exchange for mutual openness and friendship, taking some of this from her experiences in Ponyville and elsewhere in Equestria. She can become an empress only by name, and she will never accept this title.
Hence the “Friendship Empire”. Without friendship no empire. And that may be why the G5 world was thrown into darkness after the magic disappeared, as it seemed to have happened in the very heart of Equestria. Without Equestria, the global community will be fragmented.