The idea that the airlines can 'do anything they want' is not completely true. Yes, they can decide to offer a direct flight between any two airports they want, but are then faced with lots of federal/international regulations regarding that flight. Additionally the airline has to believe that the seats in the plane would be filled, otherwise why offer a flight if will be a money looser? Surprise, an airline is a company and has to receive more revenue from ticket sales than they pay in expenses, on the average, or they can't stay in business. Any direct flight has to be flown by a plane that has sufficient range with ample reserve capacity at the end of the flight. There are a lot of international regulations regarding the maximum distance a aircraft can be from an emergency field during the flight. This distance depends a lot on the type of aircraft being flown (two engine or four).
In my personal experience, I would say that most non-stop long haul flights are conducted without stopping. I've been on quite a few over the years and can only remember 1 where a stop was necessary. It was a direct flight from Chicago to Hong Kong. The weather had been bad the whole route and there was a potential weather problem in Hong Kong as well. We landed at Beijing, China and took on some fuel and waited on the ramp for about 2 hours until the situation got better. It was a good thing too, because we had to be in a holding pattern for about 30 minutes at Hong Kong because the previous delays had traffic backed up.
I have held a commercial pilot's license myself for a lot of years. Any flight I planned always had to have enough fuel for the entire route as well as sufficient reserve for unexpected circumstances. If your projected reserve is used up along the way due to weather or weather related diversions, then it's time to land somewhere and get more fuel and/or wait on the ground until things in the air become more favorable for you to continue.
What would be the potential consequences of not doing that? You could die, along with all your passengers. It's better be safe than sorry. I didn't blame the pilot for a second on my Chicago to Hong Kong flight. I wanted to arrive safely.