How big are these ramps?
Having ramps of height much more then a few tens of meters is beyond practical for most preindustrial peoples. The great pyramid of Cheops is 150m in height. These ramps would be at least double that in height, and many times the length especially if trying to avoid air friction.
Egypt had and has a major transport route which historically allowed for a single shared religion and strong state building. A strong state combined with a highly concentrated population that for periods of the year could spend time on optional projects, with major transport route that could supply a large workforce with food and supplies.
The mountain islands will have at most a strong kingdom per mountain. More likely multiple regional powers per sub-valley due to transport difficulties. So not strong state, no unifying transport.
Yet question calls for project that will need cooperation of many kingdoms over decades, maybe centuries.
If the ramps actually extend for kilometers then the costs of completions will go up to centuries.
There will be debris or even malicious opportunistic placed obstacles. How much effort will be required to be spent to maintain the track? Likely required to have a set of workers permanently keeping the track clean. Who provides workers at the ends to assist travelers? With forest mountains as frequent as the question proposes, drifting sand is unlikely, but with the very low frictions required any and all debris must be cleaned off.
If this were magically built as planned, how much would it speed things up?
It would be faster for couriers and a limited number of merchants, limited due to not being able to send many vehicles per hour to avoid collisions. A caravan over good roads can do something like 12 to 20 km a day. So maybe an hour with ramps vs a day without.
Techs needed to lower death rate.
Low friction bearings
Some civilizations didn't have wheels, it takes a bit to be able to build tolerably low friction wheels and bearings. It takes even more to have high quality low friction bearings. High speeds without good bearings will mean spectacular failures every so often. Enough to be a known thing that some will refuse to use the system.
Without some means of keeping the vehicles on the ramp they will fall off resulting in death and destruction. so this requires flanged wheels and rails or some other guide arrangement.
Rack and pinion steering
Alternative to rail would be steering that has mechanical centering via feedback. Which is not easy to invent or build. Poor implementations will result in deadly failures. Without the self centering positive feedback loops and no rails vehicles encountering a track non perfection frequently go off the track.
Project completely infeasible.
The project is far too expensive for multiple reasons.
- Requires multiple near or post industrial technologies to avoid high death and or loss of vehicles.
- Requires ramps that will cost enormous extremely long term investment
- Considering a centuries long construction time and very limited benefits, The return on investment is below zero almost certainly. There is some benefit of look how awesome we are if it is completed.
- Requires long term multi-generational international cooperation of sovereigns
- Requires strong unified states with good internal transport to be able to construct and maintain.
- Requires different geography then what is described in the question.The mountain countries will not be unified enough to need better transport.
The extreme costs and the cooperation required are going to be deal breakers. Distant secondary is insufficient tech to make it safe.