What's the purpose of yawing?
From a totally practical standpoint, let's say you're in a small tricycle gear aircraft with a freely castoring nose wheel (or a tail dragger) and you're starting your takeoff roll in a calm wind. When you bring the power up, the aircraft is going to want to turn left (why is another question), in other words to yaw about its vertical axis in a counter-clockwise direction, and head for the grass off the left side of the runway. You counteract that adverse yaw by using right rudder to keep the airplane straight. Initially you might have to use some right brake as well until there's sufficient air moving past the rudder. If you had a steerable nose gear, you wouldn't need the right brake.

You reach flying speed, apply up elevator, and lift off. As the airplane rotates about its lateral axis, there'll be some additional adverse yaw as a result of that rotation (again another question). Even if you had a steerable nose gear, that would now be useless as the nose gear is no longer on the ground. Your means of continuing to fly straight ahead is to counter the adverse yaw with rudder, and you would continue to use right rudder as you climb out. If you don't, you'll start turning left.

You reach the altitude you want, level off, and trim for level flight straight ahead. Then you decide you want to turn left. You start the turn briskly with left aileron, but you forgot to use any rudder. If you were looking at the ball on the bottom of the turn and bank indicator, you would see it shoot left. If you had used left rudder while initiating the turn, that wouldn't have happened. You would have started a coordinated turn.

Now you're coming back to the airport, and there's a crosswind from the left. You decide you want to counter that crosswind by slipping into it. In other words, you want the airplane to travel sideways at a speed that matches the crosswind while still having your nose pointing straight down the runway. So, you lower the left wing and to keep the airplane from turning, you use right rudder to keep the airplane aligned with the runway. You match the crosswind by adding or decreasing your bank.

There are other uses of rudder, and especially in aerobatics.

I once flew a few loads of skydivers. The jumpmaster sat behind me, and to help him in positioning for the drop zone, he wanted flat turns. In other words, he wanted the airplane turned while keeping the wings level. So, if he wanted a left turn, that meant left rudder and right aileron. Uncomfortable from a pilot's standpoint.

Finally, back in the 1960s when I was working on my instrument rating, I had an instructor who taught that the best way to track a localizer in close was to use rudder only for small corrections. Personally, I don't like that method, but it's one way of doing things.

A useful thing, the rudder. You need to be able to directly control movement about all three aircraft axes.