However, the requirement of the high thrust disappears once you finish the vertical climb. There's no danger of falling back to ground once you reach orbit. What you need at this stage instead, is to add velocity (deltav) to the craft to change its orbit/trajectory. This can be done even at very low thrust, because you have all the time you need. The limiting factor now is that you have only a finite amount of propellant onboard. You want to add as much deltav as possible before it runs out. A high thrust doesn't help because the engine will simply consume the propellant faster and exhaust it before you get the required deltav. This is where specific impulse comes into play. The maximum deltav you can get is proportional to the specific impulse of the engine (see rocket equation for details). As you can imagine, high specific impulse is critical for space missions requiring high deltav, like the New Horizons spacecraft that imaged Pluto or the Parker solar probe (interestingly, getting to the sun is harder than escaping the solar system). Rockets/jets with low thrust and high specific impulse are called sustainers.
The general trend seen is that specific impulse drops off as thrust increases. For example, the space shuttle solid booster has Tmax = 15 MN, Isp = 268s, and space shuttle orbiter cryogenic engine RS25 has Tmax = 2.28 MN, Isp = 452s. Meanwhile, the NEXT xenon ion thruster used in the DART mission has Tmax = 236 mN and Isp = 4200s. Note that the thrust has changed from Mega newtons to milli newtons. You would hardly recognize it if the ion engine thrusted against your body.