Consider a sounding rocket that launches its payload to several hundreds of kilometers of altitude, straight up. Imagine that this payload at apogee then points itself accurately and has a propulsion system that accelerates it by about 8 km/s to enter and stay in orbit.
Would it make sense to launch to orbit that way? Since it has never been done AFAIK, what are the drawbacks with it? What fraction of the mass at apogee would have to be devoted to the propulsion?
Since Israel launches its payloads to the west against Earth's rotation, for reasons of international politics, would it make sense for them to rather launch straight up as a sounding rocket before orbital insertion? And would it in general make inland space ports more attractive for range safety reasons?
If orbital insertion at apogee fails, wouldn't it be relatively easy to recover the parachuted payload for another launch attempt? As in no heat shield required. Compared with a payload misplaced in orbit with today's common kinds of launch failures.
Now, consider the payload of a space gun (or Verne gun or Newton gun to honor the concept inventors) that is launched straight up without any orbital speed component. Suppose it has a solid rocket engine, or some other non-fragile propulsion method (surviving the violent gun shot acceleration, as the payload of for example fuel), that then accelerates it to about 8 km/s required to enter and remain in orbit. And the gun could launch many small payloads frequently at cheap electricity bill costs. Would that make sense in competition with conventional chemical launchers?