Quote by Passionflower
What has GR to do with this?

Well, working with just SR is kinda like me telling you calculate integrals and differentials, but not letting you use the fundamental theorem of calculus to flesh the structure out properly.
SR is great because the mathematical form doesn't require you to keep track of multidimensional tensor systems, but it's just not the same as the richer understanding you gain when you include GR into the structure.
As for the inertial frame, if you were flying from here to Betelgeuse you would need to accelerate until the halfway point and then decelerate the rest of the way in order to reach relativistic speeds such as we're discussing, presumably some sort of nukepusher drive or maybe an antimatter pulse engine.
In such a scenario, yes, the inertial frame is a hypothetical, there wouldn't be a period where you would be able to claim you were at rest, much less that your frame hadn't been boosted compared to your origin frame.