My understanding of drive assist is that it's intended for a throttle that spring returns to centre when you let go of it, and nudging forward is like cruise control, it increased the set speed. With Drive assist off the throttle just sets the speed to whatever setting the throttle is at (like a car throttle IRL) so it's more about what controller configuration you use than how the SRV handles. ...
Before disagreeing with you I decided to experiment last night. So, your initial statement is basically wrong. When using a throttle (i.e. an axis) then the engine speed is determined by the position of the throttle, no matter if DA is On or Off. (There used to be an argument that DA Off let you get to a higher speed, I did not find that.) The only noticeable difference is that when moving your throttle to zero, the SRV takes it's time to come to a halt - in fact this imprecise stopping is exactly why I never use DA Off.
When using digital throttle commands (keyboard assignments in my case) the DA On acts like your first statement - forward commands increase the set speed that the SRV will travel at - DA Off means the SRV will only move forward (or back) as long as the key is pressed and will slow to a halt if key is released.
I have never tried using mouse so can't comment on that and presume that since the triggers on a controller return to zero when released I assume that (or using bumper instead of trigger) is why DA off would be better in that case. (I know in Forza etc the triggers control throttle and that works like that, only moving while the trigger is held
*.)
* EDIT - unless there is a way to change the controller action in Forza which I have never looked for.