Did a search, didn’t find this.
It bugs me when in TV/movies a big shot goes to a restaurant (sometimes where tables are booked months in advance!), and because of who they are, can get a table despite just walking in the door without a reservation.
Is this really a thing? If so, where does the table come from? Do they boot a reservation and just deal with the bad press?
I think it’s more that restaurants with VIP customers (not necessarily famous people, but high-spending repeat customers) might keep a table in reserve in case one walks in.
They get gushed over in the bar until the very next table departs. Whoever had that reso, and is waiting, gets shined on with apologies, (they’ll blame a new guy, someone’s Mom died, etc!) and comp appetizers and such. Everything reso now runs late. Somehow everyone muddles through.
Restaurants manage with a variety of tactics. One with frequent VIP clientele will hold back tables just for the possibility. They can push peoples reservations back and make excuses. They can cancel reservations. They can reject the VIP.
The managers need to calculate decisions on the fly. Sure it’s bad press to cancel reservations. It’s also good press to have celebrities in your restaurants. Rejecting important people can also end up being bad press. Important customers may bring more income than you’d ever lose if an offended party swears your restaurant for life.
There are a few restaurants I frequent where I’ll always get moved up on the wait list. I’m no one special, just a repeat customer they don’t want to go elsewhere to avoid a wait.
Is it really a common thing, or is much more made of it in mass media?
It sounds like you’re asking about some trope you’ve seen on TV/in the movies - sure hip/high end places in NYC, LA, etc. might have to worry about it, but celebrities unexpectedly popping in are just not a problem for 99%+ of eateries in the US 
We got seated in the window table. That table had been held back for VIP customers. When some real IP customers came, they opened up the upstairs room, and moved us into it.
That was at an expensive restaurant with a classy clientele. At the places I normally go to, a VIP that arrived late would sit next to the kitchen door, same as anybody else.
Even in the movies, how do you know that the reservations have been booked so far in advance? Or rather–how often have you seen this in the movies, where the dialog makes it clear that people have made reservations far in advance, and they’re being pre-empted by the big shot?
After all, famous people aren’t the only ones who walk into restaurants without reservations. Sometimes the restaurant just has space anyway.
In my experience, the trope is more that they are immediately recognized and served faster than the average person would be without a reservation. Can you site some specific movies or TV shows where this happens?
One time that over 70 of my relatives descended on the same restaurant without any planning (or rather, despite a lack thereof), when the owner realized what was happening he had the smaller room opened and stashed us there. It’s not uncommon for restaurants to have more than one room: unexpected reservations which Must Be Admitted can then be sent there or, if those people are the kind who like to be stared at, they can be put in the main room and someone else divested to the sides.
I’m impressed ^ by any restaurant that has a side room that can accommodate 70 people. Even the classiest restaurants that I have been to here in San Francisco generally don’t have that kind of extra space.
Back in 1992, Spy magazine tested* this out: Big Shots Never Wait.
*Obviously they couldn’t test it with real big shots; they called various restaurants pretending to be the assistant or secretary to some celebrity and asked for last-minute reservations.
Doesn’t seem like a particularly controlled experiment. And it’s not like it would have been hard to do—all they needed to do was call a couple minutes earlier, trying to make a similar reservation on behalf of someone non-famous.
Official occupancy wasn’t anywhere near that high, the “stashed” is pretty literal. The waiters and us teens set the tables and chairs, waiters set the tablecloths, then we sat down in order of arrival (spots with easy exit were reserved for the oldest ladies) and passed down the plates, glasses, silverware…
Customer: What if the President of the United States came here and wanted a table? Would you tell him there’s no table available?
Maitre d’: No, we’d find a table for the President.
Customer: Okay, give me his table. He’s not coming here. I just saw on the news he’s at Camp David for the weekend.
I’m not a VIP, but I used to visit my local Indian every week (and brought friends there too.)
So I was a valued customer.
One Saturday evening, I was running late and really wanted my favourite food. So I dropped by the Indian. They were completely full - but when I asked politely when a table would be free, the manager produced a card table and chair from a back room and squeezed me into a corner.
I really enjoyed that! 
in Goodfellas mobster Henry Hill gets a table setup for him right in front of the stage. You can hear others ask why he is skipping the line.
IANACelebrity, but we’ve walked into a packed restaurant without reservations and the owners quickly moved a table from the back for us. We were just regular customers and the VIP treatment led to us stopping there a bit more often.
n/m
Not just that, but it was Henny Youngman. 
And if you’ve never seen the tracking shot in which that occurs, you should.