On my usual route back home I travel a busy street with center turn lanes and bike lanes. The center turn lane makes the left turn back into my housing area much simpler and safer. I ride the bike lane until getting close to my turn, wait for a clear space in traffic, signal and move to the center lane. Then I can adjust my speed as needed to make the left turn when clear, without having an impatient driver behind me while I wait to turn. Actually, this is the same process I use when driving this route. The "cut through a lane of busy traffic" situation can be done as safely or dangerously as the rider chooses. In this case a stop light several blocks back breaks up the traffic flow and it is not an issue.
I don't understand the reference to MUP trails - maybe it is in regard to a particular local situation.