What "single voltage, two wire secondary" means, is that you are not actively using the center tap. Don't count the EGC as one of the two wires, but DO COUNT the neutral. The alternative is 120/240V as the secondary voltage, which is a three wire secondary. Consider 240V straight, or 120V straight. You abandon the center tap, if there is one at all. You configure the taps of the transformer, so you are only using one voltage setup on the secondary.
The rules of 240.21 that allow you to not have secondary side OCPD, require that you have a topology that qualifies. To qualify, the transformer topology must be set up so overcurrents line-up winding-to-winding, so that faults don't redistribute onto the primary windings and go "unnoticed" by the primary OCPD. Delta:delta three phase transformers also qualify, as long as there is no centertap either. Anything with a wye or centertap doesn't qualify.
I use the term "protect by proxy" when describing this situation. Given a 480V primary to 240V secondary transformer, a 15A OCPD on the primary effectively acts as if it were a 30A OCPD on the secondary. It can do this, as long as there is no possibility to redistribute the current on the primary of the transformer.
If you had a centertap, you could draw a 50A overload to line 1 to neutral, while applying 0A line 2 to neutral. This becomes 12.5A on the 480V primary. A 15A OCPD on the primary would not measure this as an overload, and therefore not trip. If you are counting on only 30A worth of conductors on the transformer secondary, this 50A overload would exceed their capacity.