There are three jobs an auto pilot/auto thrust (or auto throttle) must perform:
- Determine the aircraft pitch (and auto trim as needed)
- Determine the aircraft bank (to seek desired heading/course)
- Determine the aircraft thrust
Without an auto throttle/auto thrust, we remove item #3.
Another way to look at it, which is quite un intuitive is to understand the various possibilities of pitch vs throttle usage.
During climb, typically we want thrust set at a fixed maximum safe level and pitch is changed to sustain an optimal (or ATC mandated) IAS/Mach speed.
For that purpose, FADEC is enough to keep the throttle at that max safe level.
During optimal descents, we want the thrust levels at flight idle, and pitch is again used to maintain an optimal IAS/Mach speed.
During cruise we can either be thrust limited or airspeed limited. If there's enough excess thrust to keep airspeed, the thrust levels will be finely controlled to achieve a certain airspeed, or if there's a small thrust shortfall, max safe thrust levels are kept, and airspeed fluctuates with turbulence/changes in temperature and other factors that either change real thrust output or little pitch changes are needed to maintain altitude.
During approach what we often have is seeking a certain speed and a certain descent ramp (resulting in a required vertical speed), which requires thrust to the nearly always changing to achieve all of those two targets simultaneously. So an aircraft without auto throttle will require constant little thrust changes, but the actual vertical profile can be kept by the auto pilot, just respond to airspeed changes.
With modern EFIS, there's the airspeed tape that has a 10 second trend tape. This tells you where the airspeed is predicted to be 10 seconds from now if nothing else changes. So as long as airspeed is close enough to target speeds, just add thrust if the trend line is negative (until it zeros) and reduce thrust if the trend line is positive (until it zeros). If airspeed is a few knots off, add just enough thrust that the trend line gets back to your target airspeed just about 10 seconds from now (or perhaps have the trend line be twice as much as the deviation so you get be back to normal 5 seconds from now). That's actually quite easy to do with the trend line.
Autothrottle is quite important if you need to keep a precise thrust level to finely optimize fuel consumption. On smaller private jets that's usually not critical.
So the auto pilot does fly the VNAV approach or VNAV profile, without an auto thrust/auto throttle, your job is to control the airspeed, which is usually far easier with the trend line.
A related useful information is that on the top of the PFD (primary flight display, the one with the horizontal attitude, airspeed+altitude tapes) if you look on the top, in aircraft with auto throttle/thrust you will see 3 columns:
The left one shows what the auto thrust is doing (idle/thrust reference/air speed/...)
The center one shows the lateral navigation (heading/course/lnav/localizer/rollout/...)
The right one shows pitch control (altitude holding, vertical speed, speed, vnav, glideslope, flare, ...)
On aircraft with EFIS but no auto throttle, I think the left column is still there, just to tell the pilot what to do with the throttles, like a nice teacher.