Military prowess is one necessary aspect of a competent ruler, although far from being the most critical, in my opinion. Compassion towards one's people and a sense of stewardship is what I believe is needed most, as well as economic knowledge, and a good grasp of diplomacy to prevent a war or conflict before it can begin.
Princess Celestia has demonstrated all of these in sufficient measure. We've little knowledge of Equestria's inner workings, but based only on what we've seen it would appear that poverty is either nonexistent or at a respectably low level. Even the Pies, rock farmers in the middle of nowhere, had a decent house on the inside, it's only their chosen profession that kept them living amid such desolation. Assuming that she makes economic decisions with an appreciable impact on cities and towns throughout the land, I'd say she's handled this part of the job quite well. As Equestria is not at a state of war, even with the Changeling kingdom, I'm going to say she's also doing well in that regard.
The Mane 6 are mostly ordinary ponies if one was to take away the Elements of Harmony. Without them, they would have been unable to save the world when Nightmare Moon or Discord returned. However, these were once controlled by Celestia and Luna. If they eventually passed from the princesses to this band of friends, they'll eventually pass to another set of ponies or back to the princesses once the Mane 6 live out their days. At least that would make sense and is what I'm going with for now. Without the elements, Celestia and Luna are still more than powerful enough to fend off whatever mundane threats pop up. The Mane 6 can be on call for the world-threatening catastrophes. I don't think any one of them or the lot currently possess the wisdom and temperament to take the reins of Equestria anyway.
The Royal Guard aren't needed for the princesses' protection. There's nothing they can do against an assailant that Celestia or Luna can't do themselves. For the most part they're ceremonial and guard the castle grounds, and most likely serve as the police force of Canterlot; perhaps also abroad in a limited capacity. Shining Armor, while he could be a competent soldier, hasn't done anything else to inspire me in his abilities to lead a nation. Cadence is someone I would trust to rule given her affinity for pleasing others and inspiring love, while keeping a cool head under pressure.
Unless I was to make might the paramount concern, which I'm not, I believe everything can remain as it is. Celestia and Luna are well-rounded rulers, have saved the world several times on their own prior to the birth of the Mane 6, and have centuries of experience building and maintaining this kingdom, garnering the adoration of their subjects.