Ryan,
It looks like you agree with Sean, whom I agreed with earlier as well, that location and position of bunkers is more important at the end of the day than style. But, I am not sure I myself go as far as you with style having no impact on playability.
I understand that in this post you are probably referring to if they simply changed the existing bunker edges at Riv to the ragged style and yes I agree, that wouldn't have very much impact - on shots played out of the sand. The only issue would be that more balls might hang up in those additional lower tongues of grass that are currently sand ( and yes they will get comments on that). Otherwise, there are several ways that bunker style can impact playability that you have to be careful about. In fact, many of the courses I assist with renovation reason to me about how they do not like the playability of the bunkers.
Some styles that are employed might contain movement or slope within the bunker floor (sand). This effects playability and is one of the biggest complaints I hear at private clubs especially. Some of the awkward stances that result can be brutal.
Some may consider depth of the bunkers a style choice as much as function or whatever. If you go into an existing course and introduce a bunker style that requires greater depth to the bunkers than what was there before, playability is altered. An although most of us would say the players/members will adjust, most never do.
If you go to a course that has smallish greens and green pads and you decide to push the greenside bunkers in tighter against (under) the green, you need to be aware of the types of shots that are required to get out of those bunkers effectively and weigh things like the sand type and bunker depth again to determine if you can.
It is a fine line. But a hazard is a hazard, is a hazard and lets hope they complain!
It is great to talk about bunkers and not only about if the bunker styling could be the winner of the beauty pageant!
DbD