How is it that absolute encoders eliminate the need to home an axis? I guess the answer depends upon the type of encoder. There are various approaches to absolute encoders that may or may not retain “absolute” position value. One type simply offers up a value representing rotational position. Often this is 360 degrees with some odd amount of resolution. Beyond shaft rotation it is the controllers responsibility to maintain actual position. Beyond that there are absolute encoders that can track position to XX revolutions and report those values via a serial connections.
For linear encoders there also a variety of ways to do absolute or give you absolute like results. The trouble here is telling us that you are using absolute encoders really doesn’t tell us much of anything.