What you typically do at your table is not typical of play in general.
Most published modules would disagree with you. The majority of ones I've played in or looked at take you far from home, several of them while you are still level 1 or 2.
The background feature, Criminal Contact, doesn't say your contact is always present in the same city where you happen to be. I can see why you might think that would be stupid, but that's not what it says. It says you know how to get messages to and from them "even over great distances" which it sounds like are involved if you're in a city of which you've never heard. Surely, the PCs aren't the only contact between where the criminal contact is located and this distant city where they happen to be at the moment. I think that would be stupid.
I never said the PC had a criminal contact in any city they were in, my player did. But I still disagree that you can always get word to them. You've been in port for half an hour, how does that happen? Go to the local Criminals-R-Us and send a telegram? What if you're playing Tomb of Annihilation where you rarely interact with any humanoids who aren't trying to kill you, I don't see how you're getting a message to anyone. Train a parrot?
Why wouldn't they? As they say, breeding recognizes breeding.
A noble is just a person with a title, there's nothing special or magical about them. I don't believe in the divine right of rulers. Historically many members of royal families were quite inbred and unhealthy.
Why, do you think no one ever sent messages? You don't have to be notorious to send someone a message. Neither should getting a response rely on there being a world wide broadcast. The feature contains suggestions of what the means might be of sending and receiving messages if the table is having trouble coming up with ideas of their own.
I'm not sure what you're getting at. I was talking about the charlatan fake identity feature being largely pointless in an area where no one would recognize you in the first place. In addition almost all the features rely on being easily recognized and associated to some social standing or "knowing someone". That doesn't work if you travel outside of your sphere of influence.
I'm not sure what you're saying is not automatic. Assuming you're talking about the Entertainer background in the PHB, By Popular Demand says you can find a place to perform. Surely, that's what entertainers do - go to different cities in some of which no one's ever heard of them and do performances there. I don't think it's a stretch they could get free room and board from the venues in exchange for their nightly performances. Most taverns like to have entertainment because it brings in customers. It also says once you've performed in a place, you become somewhat of a local figure there, but at that point it's no longer a city that's never heard of you, so I'm not sure what you're saying here.
If some pop singer went to an area dominated by (random genre here) the blues, why do you think they could automatically get a gig? Is someone who is a concert pianist going to automatically find a job at a place where there are only dive bars? If you're playing Descent into Avernus you may be having a devil of a time, but I doubt your performance skills are ever going to get you a night at the local hot spot in Avernus.
I'm sure they appreciate you being upfront with them.
Backgrounds and how important they are, whether they can be a part of the bigger story is something I think should be discussed in the session 0. I just had someone join saying they wanted to play a failed apprentice (had studied under a wizard, became a druid) so we figured out a story that makes sense and may play a bigger part in the ongoing campaign. I say may, because it's up to the group what they pursue.
Some people care about backgrounds, some don't. Most of the time it's been my experience that it's just a way to get a few extra proficiencies.