Three days is the shortest trip to Transylvania that does not feel like a stopover, and this is the route that uses them best. It stays in the south, it moves once, and it spends the middle day where the region is at its most itself — in the villages between the towns rather than in either of them.
Why this order
Sibiu first, because it is the easiest place to land in and the gentlest introduction: compact, pedestrian, and readable in an afternoon. The villages second, when you have enough context for a fortified church to mean something. Sighișoara last, because it is the smallest and the most concentrated, and because arriving in the evening — when the day visitors have gone and the citadel is lit — is the version of it worth having.
Reverse it and the trip still works. It just peaks earlier.
What this route deliberately leaves out
Brașov, Bran and the mountain roads. Not because they are not worth it, but because adding them turns three days into a driving holiday. They belong in five days, and the extra two days are the best-value days in any Romania itinerary.
If you have three days and want the mountains instead of the villages, this is the wrong route for you — take the Făgăraș side and accept that you will see one town properly rather than two.