Doesn’t anyone remember the Arlo Guthrie song “Coming in to Los Angeles”? The opening lines go something like this:
Coming in from London from over the pole
Flying in a big airliner
Anyway, the point is that most flights don’t parallel the equator. If fact this would be an impossible way to get to any desination not on the same line of latitude as the departure airport. If you parallel the equator your latitude never changes. I suspect what you meant to say was that the angle with respect to the equator never changes. This would make the true course of the aircraft constant from the departure airport to the destination airport.
But as you and JonF pointed out, these are not the shortest routes. In fact, althouth I’m not sure if I can prove this, on a long flight that traverses many meridians the constant angle route may be several times longer than the great circle route. I believe great circle, or near great circle, routes are by far the most common routes traveled by airlines.
Politics may be the only reason that great circle routes are not used. There needn’t be any land naviagtional aids along the route in order for a airline to navigate over it. In the past the INS (inertial naviagtion system) was sufficient. It is now being replaced by GPS. Landing sites can be a problem. ICAO (international civil aviation organization) and the FAA have some rules about this. Airlines must be within a distance from an airport that allows them to fly there on one less than all engines in a certain amount of time at all times.
For twin engine airliners this used to be 90 minutes. So at all times a twin engine airliner had to be within 90 minutes flying time on one engine from an airport it could land at. This eliminated many routes for twin engine international airliners. Now new regulations are being granted on a per model basis to extend that time. For four engine airliners, I’m not sure what three-engine-to-an-airport time is, but it is long enough to allow nearly all routes for these aircraft.
Visiblity is never a problem, airlines can fly through zero visiblity. Some can even land in zero visibility. Turbulance is more of an altitude problem, not a latitude problem. I don’t think the 35000 feet above the north pole has any worse turbulence than anywhere else 35000 feet up.
JonF I think that article title is misleading. Airlines have always used routes that traverse high latitudes. Now more of them are open due to Russia opening its airspace. I seem to remember that quite a few years ago a western airliner was shot down when it was flying over the pole and wandered off course into Russian airspace.
To answer the OP, yes airlines can use meridians. If two airports are on the same line of longitude then the shortest route would follow that line. This is because all lines of logitude are great circle arcs. Only one line of latitude (the equator) is a great circle.