Following this answer. This is actually a set of three different questions:
How often airlines "wastes" money, by putting long-hauls (widebody aircrafts) on regional or domestic routes?
Are there any (economic?) arguments for doing so (except special cases: like no other kind of replacement for broken small plane)?
Is there any example of any regional route, that is served by long-haul on regular basis?
But, I think, that all of them can be answered with one, quite simple answer.
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.
The Boeing 747SR is a short range version of what would normally be considered a long-haul aircraft.
To specifically address question 3, it regularly serves the Tokio International/Haneda (HND) to Osaka (ITM) route, which is a flight duration of roughly 1:05. JAL 123 is a well known accident on that route.
No matter high /low capacity, airline can generate income if the plane is on the sky with sufficient passengers. That means airlines will utilise the aircrafts by maximising their operating hours.
Between long-haul flight(s) operated by large aircrafts, there may be some "gap" times, airline will operate some short-haul flight by the large aircarfts to fully utilise them.
Using China Southern as example, two of their a380s(B-6136 & B-6137) are used for short route CAN-BEK (~1100 miles) and at night they will be used for CAN-LAX (~7200 miles) and come back to Baiyun airport in the early morning of two days after (China time zone). However most of the other airlines has more complex schedules, the aircrafts used for EK857/858(DXB-KWI), the A380 shortest route(~550 miles), are used for many meduim/long-haul destinations, including MUM, JFK, HKG, LHR, SYD, BKK, FCO, BNE......
PS:Jon Story answer claimed that "long haul routes tend to have less frequent service with larger, higher capacity aircraft";however some airlines actually uses smaller aircrafts with more frequent services. Cathay have 5+ daily HKG-LHR routes (~6000miles) with b77W, exclude the night time there is approximately 3-4hrs average for each departures. Using "smaller" B777 (instead of A380) means more flexible choices for customers and the aircrafts can also be used for lower capacity long-haul routes.
I don't know if this is exactly the answer that you wanted but 5th Freedom Flights as they are called are airline and airport agreements that allow airlines to operate between two airports that aren't bases or focus cities. Examples could be Air France and KLM that operate from Jakarta and Singapore or Singapore Airlines that flies from Manchester to Munich and then onto Singapore. The only main requirement is that the flight must fly back to base. This is why usually long haul aircraft are required as the flight does fly back to the main base for the airline. Fifth freedom flights sell in either sector whether it is between the two non-base cities or between the base and another cities. This allows airlines to pick up more money and get more cash
On the other hand, long haul aircraft can be frequently used in Eastern Asia. For instance, flights from Osaka and Tokyo which is less than and hours journey can be served by 747's. The main problem with this is wear and tear this produces on the aircraft. This has caused accidents in the past due to metal fatigue and other dangers.
