Earlier quoted context omitted.
You need a second burn just to enter orbit. You burn at the top of the sub-orbital arc (opposite side of the earth) to enter orbit.
No, that's inefficient and real spacecraft don't do that for typical low earth orbits. Works in Kerbal Space Program, though. Normal orbital insertion is a single burn to orbit (with staging). With the correct initial roll and pitch, the spacecraft follows a perfect gravity turn and ends up in a near circular orbit at main engine cut off.
You surely know that, but mathematically it is unavoidable to have a 2nd burn at the apoapsis to have an orbit (with a periapsis > the initial launch altitude, minus gravity and atmospheric losses), albeit it may start earlier (while wasting a slight amount of delta-v).