Earlier quoted context omitted.
Realistically, no. I write this in the gentlest manner possible, not directed solely at you: a lot of the "see a gate agent and they'll sort you" advice seems to be coming from a place of people who either don't travel very much at all, or who travel so much that an airline employee can practically feel their level of Airline Status(tm) from half a kilometer away and will race to their aid. I fall in the third bucket…
Is the answer still no for conventional airlines? Because if have guessed the distinguishing factor isn't the amount of traveling, but the mode (budget airlines).
If the airport is a hub for an airline, you might be able to get someone to make a change, but that late at night, even that is going to be difficult, unless it is a major hub for the airline. Like, if you get stranded in Atlanta on Delta, chances are someone is around who can help you, even late at night. Same for American in Dallas, KLM in Amsterdam, Air France at CDG, Quantas in Sydney, etc.
Delta has a concept known as Red Coats, which are employees empowered to make more decisions regarding booking, but most of the gate agents are beholden to whatever the system is telling them. I’m sure other airlines have similar representatives but Delta's program is fairly unique amongst American carriers, in terms of its visibility (a tip for anyone flying Delta who has a tricky situation, especially around rebookings, is to ask for a Red Coat. You won’t always get it, but those are the people most empowered to help).
Sometimes a non-status customer can get lucky by getting on the phone while in the airport — in my pre elite status life, I’ve successfully had gate agents speak directly to someone on my phone to resolve a situation — but if it’s right before Christmas and you’re at risk for not getting home and your alternate flight is leaving soonish, you’re almost always going to be better off just booking the alternate flight and then dealing with customer service later.
But as I said in another comment, outside of LCCs, there are two distinct classes of customers for airlines. And it isn’t just enough to have spent a lot on a specific ticket (unless you’re flying international first class on Singapore or Ethiad or something — but Asian and ME airlines are a whole different world), the airlines don’t care that you paid to upgrade yourself to domestic first class or even that you’re flying international business. The people they bend over backwards for either fly enough domestic miles that they spend as much time on a plane as the crew or are people who spend at least $30k with a specific airline. I spent over $50k with Delta in 2019 (and $20k before I was grounded in March) and I still didn’t qualify for Delta 360, their invite-only loyalty tier. Don’t get me wrong, Delta has treated me incredibly well — but I’m still just one of many thousands of Diamond Medallions to them. They won’t send me someone to escort me through security when I’m in danger of missing my domestic flight (something American did for a friend who has their Concierge Key status and pre-COVID averaged $50k a year with them for about a decade), but depending on the flight makeup (depends on how many other high status people are on a flight), I’m usually going to be in the group of people auto-rebooked to a good time or booked on a different airline without having to make a fuss, in order to maintain my itinerary.