Your knowledge is correct, it will waste half the transformer's output capacity if the only reason for using a centertap is for the purpose of generating a small -1.25 V bias for the negative supply.
The center tap as described by that post is best used for an equal, bi-polar supply of + and - voltages. It gives a full wave rectified voltage at + and - the transformer's half-winding rating.
If what is wanted is a single output positive supply capable of being adjusted down to zero, then it's much better to generate a small -1.25V bias for the Adj pin using one of the many methods already described (half-wave, charge pump, zener, shunt-regulator, etc).