I've always just left it to player preference. Within reason, you can be any social class you want and have the connections you want, as long as you still have the standard starting gear. Some of the 5e D&D Backgrounds like Acolyte do include 'social support' elements, the Noble background even includes retainers.
I'm fine with this and it works, but it does seem very limited compared to other games that I've played. For example, in one GURPS Fantasy campaign, I made an heir of a wealthy merchant family. That made a major material difference for him. First of all, he was rich and had top-notch equipment especially because his family were arms merchants. Further, he could call in favors with his or related families. (Status and Wealth advantages.)
The D&D approach is definitely designed for D&D!
I'm generally not keen on 'buying' social status, or military/professional rank - it results in having the top people be less competent than the bottom people, which tends not to be true IRL. I'd rather social status be free within whatever limits the campaign sets, and rank be derived partly from competency, not bought as an Advantage. Usually it's easiest if either every PC is of similar social status, or else it's a setting (like standard D&D, or cinematic Old West) where social status does not matter much.
Overall, I'm trying for a game that is distinctly D&D, but is different than standard. It's should be a game where society and culture are important, not like cinematic wild-west where class doesn't matter. So I want to strike some sort of balance between how I've done things in other fantasy games and standard D&D. In the campaign, all the PCs do have similar status because they will all be recruited by royal authority for their work. So they will all be high status, but some may be slightly higher or slightly lower. Also, they'll have different connections because they're potentially from widely divergent backgrounds - since the empire is so vast. A respected chief from the southern desert will be treated differently than a scion of a noble family in the capital.
As for how to balance things:
1) I've also seen the problem of less competent leaders, so I'd like the "buying" to be things unrelated to general competence. This being D&D, all of the PCs would have roughly balanced attributes and personal abilities. But the extra options might include things like secret patrons, special items, helpful spirits, and the like.
2) On reflection, I might just have a unique set of Backgrounds for the setting - but where here the choices aren't just like standard choices. They'll have major advantages associated with them.