i don't yet understand how the passage of time should affect a craft's movement... one second it is at this XYZ position and the next it is at that XYZ position...
Yeah - and how did it get there? It got there in response to forces acting during that second - but these forces may not have been constant during the second.
Say I'm flying straight and level, and then smoothly pull the stick. The elevator motion is such that at the beginning of the second, the force exerted is zero and at the end it's (for sake of simplicity) full, i.e. elevator-norm is 1.
If you sample the dynamics once per second (Delta t = 1s), the motion of the plane won't show any result of the elevator at all during that first second - because at the beginning of the sampling period the force was zero, so you calculate the timestep with that value.
If you sample with Delta t = 0.5 s, you'll do the first sampling step without force, but for the second step there's at least a force of 0.5 seen, so the plane will respond - albeit in a crude way, hardly smooth.
Which is to say, the longer your sampling step is, the more sluggish the response of the plane to control input and external disturbances will be - and any autopilot not taking this (purely artificial) numerical sluggishness into account will overcorrect and get into an induced oscillation.
Which is to say, if you anticipate to simulate with potentially long sampling timesteps, your guidance algorithms need to be tuned separately to these situations. Or you need correction steps.
The simulation of the Shuttle external tank motion after separation has, if you look at the equation of motion solver, an explicit dependence on the current framerate. There are unphysical correction terms proportional to Delta t which vanish for Delta t -> 0 which compensate for the inaccuracy in the trajectory induced by not sampling the force continuously.
You need to know quite a bit about numerical math to pull these kinds of tricks out of your bag - it's clearly beyond 'just' designing an autopilot logic, which in turn is not something everyone does well.