So there must be some accounting for this propagation error, either as losses, or engineering.
What I suspect (totally not my field) is that the high power interconnects between large generators do have this triangular lag (the incoming lines lag from the plant's reference frame), but they use quadrature boosting or similar to match that particular interconnect.
T&D (transmission & distribution) result in ~6% of the net energy being wasted. I imagine phase lag "feels" like impedance, with the real component acting as resistance.
Also, it's worth noting part of the appeal of HVDC, aside from line reactance and skin effect, is you get to choose your output frequency.
Maybe active synchronisation solves this, but to my (inexpert) mind the network would still suffer from interferences at various points between power plants.
[1] https://en.wikipedia.org/wiki/Synchronous_grid_of_Continenta...
https://en.wikipedia.org/wiki/Continental_U.S._power_transmi...
So that takes care of some of it.
Anyway, synchronization is actively managed, when a generator starts up, it is synchronized to the grid adaptively.
https://en.wikipedia.org/wiki/Synchronization_(alternating_c...