Yes, there are rules for combat. But there are many cases where you can't do something you could normally achieve.There are things within combat that automatically succeed though. You can automatically move your base rate to get into close quarters with someone, for example (barring some sort of legendary interrupt action I guess). You can draw your sword automatically. You can use action surge automatically. These things just don't resolve the actual fight.
Similarly, the background traits are pretty minor effects that mostly set up other rolls or negate minor obstacles. The local populace give you shelter - OK, what next? The underworld messengers send a message for you - OK, how is it received, what happens as a result? The hobgoblin court grants you an audience - OK, can you convince them to do what you want, or even not to eat you?
It's a false equivalence to say the effects of the background traits are like automatically winning a combat. These are minor, minor things.
I'm not going to argue about infinite strawmen any more. The background features did not work for me and I didn't use them as written when I DMed. For that matter I never saw any DM allow them as written in any game I played either.