First paragraph: I see what you're saying and I think you're right.
Second paragraph: Even if you're right on this, and offhand I'm really not convinced you are because it seems like that neglects the possibility of collision, launching anything from the surface of a planet is a three-or-more body problem, featuring 1) the planet, 2) the star it's orbiting, 3) the launch body, and optionally a number of moons. But that's, ah, getting away from OP's question.
You can think of a parabola as a segment of an ellipse, yes.
But remember: A stable orbit forms an ellipse. An unstable one doesn't. And throwing an object from the surface of a planet is, sans incredible math or even more incredible luck, going to be unstable.
Anyone willing to do that probably needs the cash more than I do. Who am I to say? If I can spare it, I share it. If I can't, I still try to give a little of my time to recognize them as a fellow human being, because I know begging or just being destitute in general feels dehumanizing.
As a junior teacher, I taught summer school. The more senior teachers were doing continuing education. We all made lesson plans, prepared materials, and had mandatory professional development seminars.
First paragraph: I see what you're saying and I think you're right.
Second paragraph: Even if you're right on this, and offhand I'm really not convinced you are because it seems like that neglects the possibility of collision, launching anything from the surface of a planet is a three-or-more body problem, featuring 1) the planet, 2) the star it's orbiting, 3) the launch body, and optionally a number of moons. But that's, ah, getting away from OP's question.