Sure! You could set manual thrust in the same way you can set manual pitch trim.
But thrust would need to vary, however, unlike trim, for climb and descent.
And remember, the question asks what the most basic requirement of an automatic VNAV capability is.
Which is the most basic: auto-throttle only (one system) or pitch controller + pilot controlled throttle? (two systems - for the sake of argument, pretend the pilot is glued to the aeroplane.) In other words, which requires the least amount of interaction with the aircraft?
It's auto-throttle alone.
Yes, both methods will produce a working VNAV controller, but this is yet again one of those questions where you have to get into the head of the examiner and choose the most-right answer.
Which brings us to the point above that the question banks aren't fit for purpose because they shouldn't require mental gymnastics like this.
(Also you are quite correct about climb performance being excess thrust over weight, not gravity. Ooops. Been a few years since I've done this.)