se hace camino al andar!
Pilgrims in former times started from where they lived, using the road network of the time; more or less any old road will have been used by some pilgrim at some time. Most modern pilgrims can't or don't want to do this. Many of these old roads are now busy highways which the modern pilgrim on foot will want to avoid. In addition, most of the contributors to this forum do not live in Spain; many do not even live in Europe. So what the people in this forum are looking for is a route that will broadly follow an old road and visit historically interesting places, but which is safe and pleasant for the modern walker, and is also easy to follow for those who do not know the area, preferably by being waymarked and/or having an easily obtainable guide. Both the Levante and the Sureste do this. They are both based on the old roads from the east coast to Toledo, and then north. Like all the modern pilgrim routes, they are modern creations even if based on historic roads. Essentially the modern routes are 'marketing packages' that make things easier for the modern traveller. They all have to start somewhere, but that starting point is generally pretty arbitrary.
I would agree that the Levante going south, then west, is not very logical, but it still follows old roads, and I can't see any problem with people following it if they wish.