Doesn't this still present the problem of synchronizing time across frames of reference?[The definition of a second] does not change when you look at another person in a different relativistic/accelerating frame of reference. "It's not the units that are flexible and changing, it's spacetime itself, the actual physical reality of the universe, that changes to keep the speed of light constant." - quoting from Physics Stack Exchange
If i understand the statement, it is saying that the unit of time does not change, but the time paths it measures may vary. This shift is already a noticeable issue in communications satellites. If one imagines spaceflight at anything approaching light speed, then trying to define rendezvous times becomes a challenge. Having a ship arrive at a space station with both of their day times seemingly aligned becomes very unlikely.