Jonr,
Your statement is only correct applied to poorly insulated and small mass situations. If the mass is only enough to average one day’s temperatures swing of energy your statement applies. When the mass and insulation levels allow for a time constant that exceeds months the world changes as to the appropriate application of mass.
This is similar to the passive house standard. If the insulation level is two to three times code the total energy per day becomes so low that you can eliminate the primary heating system saving say 8 to 10 thousand which can pay for the insulation upgrade. There is more to it but simply put that is the case.
Passive house standards due not adequately consider the thermal mass in the calculations. Thermal mass has the same relationship to the structure. Once the design is passive the amount of insulation can be reduced and replaced by mass. This relationship is dependent of the local climate in the same way the insulation levels are in the passive house system. This chart shows the relationship in a specific climate. This location shows an R-100 no mass is equal to 3 feet of earth and R-10 and that at 20 feet of earth no insulation is needed. The second line on the chart shows the relative cost of the materials involved in the walls as you transition. This leads to a sweet spot for cost which can be adjusted based on the projects needs.

This principle has been demonstrated in many example homes, built in extremely cold, moderate, mild and warm climates. It has also been demonstrated in dry and humid climates. It works everywhere that is reasonable to inhabit.
Brian