I tend to care very little about the ins-and-outs of routings, and tend to see it from a mostly practical standpoint and less artistically, but I'm no architect so I'm sure I'm susceptible of
being blind what I'm not educated enough to notice. Still, where I notice routings is in the final hole, and less so, with the first hole and the turn.
I am strangely passionate about final holes, and I see very few courses that I think do them very well. To me an interaction between the clubhouse and 18th green can give a hole a character rarely seen in causal golf. If I ever have Bandon money, I would want to build a course where the 18th green was tucked into a horseshoe-shaped clubhouse (with the building in play) overlooking the green so everyone could watch people play in. Most courses seem to leave a significant interlude between the course and the bar, or just dump people into the parking lot.
I wrote about one of my favorite first holes (
#1 at Lions Muny), and the reason why I think it works is that the routing puts the first tee right in the middle of everything. That everyone at the course is watching you take a tee shot is a good way to make and easy shot feel hard, and turn a gentle handshake into a firm one (note that the middle and front tees are progressively father a way, so the pressure of being watch diminishes for less skilled players).
Returning nines is practical, but, again, I think a routing that ignores that has room for giving a course a unique personality. Anyone who knows me knows I'm a nut for a halfway house, again because I see a halfway house as rare opportunity to impart the tone/brand of a course through its architecture, and without that halfway house, you can only do that with the clubhouse.
The last thing I would add is that pace of play can be significantly impacted by routing. Looking at the subject through, I guess it should be called "gate theory" of pace, it'd be interesting to try to use the routing to add/remove "gates" depending on the current pace issues. I think it would be interesting experiment, but I don't think most people take that stuff seriously.