Governments have limited resources and so they’ll focus and optimize their spending to maximize efficiency and the same reason a bus route would be unattractive to a for profit operator would likely force a non for profit one to direct their attention somewhere else.
The best way is usually forcing the for profit operators to bid on whole regions rather than individual routes and mandating minimum service levels across the board which would prevent operators from running a bus once a day and calling it a served route.
The only way in which a government run transportation provider would not experience this issue is if the people are aware of it and are willing to pay the extra money in taxes to cover the costs of running unprofitable routes and would actively lobby their governments to spend that extra money on exactly that which isn’t likely.
This isn’t about socioeconomics if anything poor neighborhoods would have more people commuting via buses than richer ones that can afford petrol, parking and rail passes.
What bus operators like is predictable routes even if you fill only 4 busses between 8-9am and again between 5-6pm it’s a very good route because it’s bother predicable and that most of your users would likely buy seasonal tickets.
So essentially routes that connect people to places are very attractive but routes that connect people to people are not.
This means that there would be much fewer routes that connect neighborhoods directly especially within the same socioeconomic level which forces many people to change at a city center or at any other service hub to get to their destination.
This also affects commuting routes outside of rush hours and especially night buses.