I would like to have kind of a pool of road buildliness that can be spent each turn.
I'd rather not have to allocate a thimbleful of roadwork every single turn. I want to devote my attention to road-building on a per-project basis, e.g., "all right, I need a road linking my mountain mines with my primary city," and then I lay out that road.
The combination of "we want to avoid workers" and "we want more depth than roads just appearing" suggests to me that the problem with the worker system is the micromanagement. Road-building workers are to Civilization what peons are to RTS games, and people do tend to prefer post-peon resource management (Total Annihilation, Company of Heroes, Dawn of War, etc.). That and naval transports, and again, autotransportation is popular (units turning into boats in Rise of Nations instead of requiring separate transport boats).
I don't care for the idea -- endorsed by several posters -- of building roads with military units. It doesn't solve the micromanagement problem, and it creates a conflict between keeping military units in strategically good spots (or campaigning with them) and building roads. The Total War series had watchtowers built by military units for at least one game, but doing this was a weird little chore, and by ETW they had abandoned it in favor of automatically revealing the map within and aroundyour territory.
So how to automate? I don't think automated workers like you see in Civ are the right answer, since they still exist at the unit level and periodically demand attention. Instead, I propose a system where the player designates a road path (possibly with a waypoint system, as Malex1 suggests) and then cities automatically send out work parties along existing roads to build it. The work parties can get to the end of the existing road and start work in a single turn, but any enemy presence along the road back to the town will cause the work party to disperse (as Malex1 also suggests). Work parties are tiny figures and obviously not controllable units. They do not run the risk of being captured and cannot be manipulated directly -- although it IS possible to issue a stop roadwork order to a particular town, or all towns, if there are more pressing demands for the resources involved. (Presumably, they take a cut of the city's production.)
However, that's the more involved approach. I'm not sure how much of the game is supposed to be road-building. I think I'd rather be managing resources, capturing nodes, training and equipping units, building and organizing cities, researching and casting spells, waging war, etc. KellenDunk's suggestion of roads emerging organically from your trade network is the best in the thread so far. It's more radical, but it's elegant. Players wishing to devote resources to a mobility advantage will presumably still have options such as teleport spells, flying creatures, magic gates, and so on.