Assuming the DP is part of the flight plan I've been cleared for ...
then maybe what's confusing is that flying the DP is sort of like
following my flight plan with my own navigation, yet at the same time,
I'm on a vector. And doesn't an issued vector usually take precedent
over a flight plan?

But I understand now... Always fly the dogleg if you get an initial
vector from tower between 0 and 080 degrees when departing Runway 4R.
Even though you might get "cleared for takeoff runway 4R fly heading"
you disobey that vector for a few minutes during climbout. But maybe
tower says "cleared for takeoff Runway 4R fly Cicero 2 departure then
heading 040" which would sound much better to me. ... aKiley