Doesn’t this ignore the fact that earth has an atmosphere? Couldn’t you fire something that would have an escape trajectory but then decays though air resistance into an orbit?
Let's put this another way: every orbit is an ellipse. If you do not alter your orbit, you will only travel on the ellipse. The moment you stop interacting with the atmosphere, you are on a fixed ellipse. The problem is just behind you on the ellipse is the atmosphere, and if you continue forward on the ellipse you will inevitably come back to the part of the ellipse that is still in the atmosphere.
But it's not a point that you suddenly stop interacting with the atmosphere, it's a gradient, with asymmetric forces on the forwards and down directions from gravity/air resistance that are smeared over time, a bit like a non-instantaneous burn around the fast end of the ellipse; I'm not sure how well the "free motion in a vacuum" intuition holds in this case; but especially when your delta-v from the atmosphere is smeared nonlinearly over your ascent period.
Yes, you end up at the same height or lower the next time round, and will incur drag from that, but shrug, that's just regular orbital dynamics.