The large taper in headstocks is provided so you can pass the largest possible material through the spindle. Typically, a tapered adapter comes with the lathe, reducing the taper to the same size as the one in the tailstock.
Yeah, you can make one from soft steel, but it won't retain its precision very long. Each time you bump it out of the headstock you'll be inclined to mush it a little, and if you don't do a good job of matching the taper intimately, your center will be inclined to move about under the pressure of the cut. Assuming you can match the taper well by bluing, that may not be an issue. However, I don't recommend a soft adapter unless you don't expect to use it very much.
What you can do instead of using a faceplate is chuck a short piece of stock that has a shoulder so it can't move in the chuck. Grip the piece with the shoulder tight against the end of the jaws, then turn a 60 degree point on the piece. Use the chuck jaws to drive the dog and you're set to go. It saves you changing from the chuck to the face plate, which would be an offset for the time you take turning the point. That the point is soft makes little difference in this instance because it turns with the spindle, so all it's doing is locating and restraining your part. It need not be hard, in other words. Should you choose this route, save the center for future use. A quick pass on the angle each time you've chucked it and it's ready to go, dead concentric.