Multi-engine aircraft are divided by
FAR 23 into two weight classes - above and below 6000lbs, and those below 6000lbs are divided into two classes depending on Vso (stall speed in the landing configuration) above and below 61 knots CAS.
Only those twins that weigh more than 6000lbs or have a Vso higher than 61 knots need to demonstrate any single-engine climb performance at all for certificaion, and the requirements are pretty meager. Basically the regulation says that these aircraft must demonstrate
a single engine capability at 5000' (ISA) with the inop engine feathered and in a clean configaration.
The
only requirement for an aircraft less than 6000lbs, and with a Vso less than 61kts (like the Aztec) is that its climb performance (positive or negative)
be determined.
There is nothing in the FAR which says a light twin aircraft must fly while in the take-off configuration with one engine inop - and so attempting to train for that is a nonsence applied by instructors who have a half-arsed understanding of airline operations, which are on aircraft in a totally different category.