Ableton Link is, unlike ReWire or Midi Clock, a very loose sync method. In it’s core it only syncs tempo and beat/bars (even looser, Ableton often refers to it as simply “phase”).
So it’s by design not syncronizing sequencer time lines, but only tempo and basic timing.
So there is no way to sync sequence positions, but a later update then indeed added start/stop syncronization. We’ve skipped this for now for two reasons: I wasn’t sure how many people will make use of Ableton Link at all. And I always imagined this to be a helpful aid to loosely jam with others in the same network. Not as a replacement for ReWire or MIDI clock. It wasn’t made for that.
But of course having start/stop sync by default disabled, but just having the option to enable it, indeed will be nice. We’ll try to get that into a future update, when we see that there’s demand for it.