Having a speed gradient across the lanes is for limited-access divided highways only. Left lane / right lane == fast lane / slow lane is not applicable to ordinary streets.
Under free-flowing traffic conditions, there is no such thing as the "fast lane." What you're thinking of is called the "passing lane." If you are not actively passing someone in the cruising lane, then you need to get out of the passing lane, right now. If someone in the cruising lane is next to you and going the same speed as you, then you need to slow down or speed up, move over, and resume your cruising speed. There is no excuse for cruising in the passing lane.
"(b) If a vehicle is being driven at a speed less than the normal
speed of traffic moving in the same direction at such time, and is
not being driven in the right-hand lane for traffic or as close as
practicable to the right-hand edge or curb, it shall constitute prima
facie evidence that the driver is operating the vehicle in violation
of subdivision (a) of this section."
That section has numerous exceptions, as does the referenced "subdivision (a)." The point is there are many valid reasons why someone would come to a dead stop in the left lane of a multilane 2-way road.
On a limited-access divided highway there are far fewer reasons, limited only to emergencies, and the left lane can be legitimately considered to be the fast lane.