Is it right to think that after the preload is set, and the stem bolts are tightened, the stem cap becomes redundant? Will the preload be held fixed by the stem? If so, does that mean the stem cap can be removed after preload is set?
Yes this is correct. Once the stem bolts are tight, they hold the system together. The top cap can be loosened without releasing the preload. You could try it out and you should find that the stem remains fixed and no play will develop.
You'll still need the top cap next time you want to preload the headset, so perhaps not redundant... maybe furloughed is a better word ;)
As noted, the cap is theoretically not needed to hold the stem in place, but in the rare situation you need a stem adjustment on the road/trail you'd have a hard time of it. I've removed a spacer above the stem to be used on a different bike after tightening the stem bolts and never had a problem riding on singletrack. But I put the cap back on, for the reasons below...
Mud & water could certainly enter an uncapped steer tube, but the bigger consideration for me is that in a crash, an open tube like that will want to take "core samples" from anything soft and squishy (like you, compared to the tube material). Handlebar end caps are more of a concern here, but that is why NICA (the youth MTB league I coach with) requires the steer tube to be capped to ride or race with a team.
"Furloughed" is a great picture, but "re-purposed" as a dust & safety cap is how I'd put it.