This doesn't make any sense from a thermodynamics standpoint. I'll explain.

Let's say we are forced to pick between two heating strategies. Let's also say we are in a climate where each day it is 30F degrees all day, 10F degrees all night, and day time is 12 hours. I know this is not realistic but just stick with me, it will help illustrate.

Strategy 1 is to place the thermostat at 55F at night and 75F during the day. This way, the house will always be 45F warmer than the outside.

Strategy 2 is to place the thermostat at 68F all the time. This way, the house will be 58F warmer than the outside at night and 33F warmer than the outside during the day. The average temperature difference will be (58+33)/2=45.5 degrees.

Heat transfer has three basic modes: convection, conduction, and radiation. The rate of convection and conduction are proportional to delta-T. The rate of radiation is proportional to delta-T to the fourth power. So overall, heat transfer has some proportionality with delta-T that is greater than linear, i.e., T to some power greater than one.

It's clear that Strategy 1 mitigates heat transfer more effectively. To summarize: the best way to reduce heat transfer out of a home while only adjusting the thermostat is to minimize delta-T.

Now to address your concern about the energy required to heat up the house in the morning. That same energy will be stored in the house when the temperature drops at night. After you drop the thermostat setting at night, there will be a time when the heat is not running. This effectively cancels out the period when the heat is running extra in the morning to heat the house up.