What are the benefits of long-haul airplanes servicing regional routes?
TL;DR You're confusing concepts, planes come in high/low capacity and range, routes come in high/low demand and long/short haul distances. A high capacity long range aircraft can operate very profitably on a short haul, high demand route... a full 747 would actually be more profitable on a 1000km route than a full 737, because although the 747 uses more fuel, it also carries a lot more passengers.




You're assuming that putting a big plane on a short route wastes money. Airlines don't work in miles per gallon like you or I do with their car... they work on income/expense. I could fly 747s on 100 mile hops all day, but if they're full of 400+ passengers each paying more than 0.25% of the running costs of that flight, I'll still make money.

If they could have used a smaller aircraft, it might waste a
little money carrying the extra weight, but you seem to be
over-simplifying things

I'm guessing this question is actually more along the lines of "How often do airliners run an aircraft that isn't completely full, and how much of that time could they have actually run a smaller aircraft?" To which the answer is "Usually, and not very often"
The economics are about running the whole system as a profit. If I have enough flights in summer that fill the aircraft, then over 12 months that bigger aircraft (highly profitable all summer, breaking even all winter) may make all money than a smaller aircraft making a small profit all winter, and a small profit all summer, but not being big enough in summer to take the entire potential demand.

Essentially, though, airlines are in the business of getting the "best fit" for their fleet. They aren't trying to get a plane in every size to have the perfect profit ratio for each flight, they are trying to get a suitable plane on each flight. This involves moving planes around as routes change etc. In an ideal world you'd run each plane exactly full of every passenger who wanted to fly on that route. In reality, we probably want a plane which is just slightly bigger than that, to cope with the small amounts of extra demand
Again you're seeing "Long haul" and "Short haul" aircraft as different concepts. They aren't. There are only high/low capacity aircraft and high/low capacity routes. Long haul routes tend to have less frequent service with larger, higher capacity aircraft (if you're travelling for 18 hours, you don't need a service with departures every 3 hours). They also tend to involve people travelling from "The UK" to "Australia" for example, so one big plane can cover all of that, and split to smaller aircraft to disperse them

Short haul routes tend to have more regular service and smaller
demand levels, partially because people are less likely to want to depart at the same time every day, and partially because they can be more fine grained - you can go from an area of one country to an area of another.

What you seem to miss is that these things are not mutually exclusive... with enough demand, larger aircraft can run short haul routes very profitably. The fact a 747 is usually profitable on long haul flights, and the fact the demand on short haul routes do not usually have enough demand for such a large aircraft, don't mean that one could never be profitable if enough people wanted to fly on it. There are airlines using 777s for example for fairly short haul journeys, very profitably, all over the world.