Last year I replaced the old Honeywell thermostat in my home with a programmable one. I figured that the set back feature would save me some money during the heating season. I don't think it did. Then this summer I kept using this thermostat for the cooling season, but I kept it at a constant temperature. My heat pump seemed to run for only a short time, but it ran often. The temperature in the house never changed from the setpoint, which is what I assume a digital thermostat is supposed to do, but I became a bit concerned about the constant cycling of the heat pump and I decided to switch back to the old thermostat (mercury type) a few weeks ago. Within a few hours the humidity in the house dropped 12-15 % to about 40. This never happened with the programmable thermostat. Now back in the winter, when I set the thermostat back, it seemed that when it returned to the "normal" setting it always ran for a few minutes, then it called for the auxiliary heat.
So it is my opinion that setting back a thermostat on a heat pump is really not a viable option because the resistance heat required to raise the temperature cancels the savings attained during setback hours. And that precise control during the cooling season doesn't allow enough run time to properly reduce the humidity in the residence.
Anyone else share these views?

No

You have some interesting points:

If you want/need dehumidification, you need to purchase a stat which will try to dehumidify. It does this at the expense of exact temperature control. Lowering humidity is best accomplished by lowering fan speed. Hvac1000, I believe has posted a schematic where a humidistat controls the fan speed. High/low. It makes sense.

Em heat usually can be turned off and/or tied to outside temperature. The temperature set in the stat and a corresponding outdoor sensor will lockout the compressor below a certain temperature. The actual algorithm seems to be guraded among manufacturers as to when emg heat kicks in. Two ways seem plausable:
1) compressor is locked out
2) It took to long to raise the temperature
3) Difference between Setpoint and Measured Value is Large.

The adpative control algorithms in some tstats try to make the SP = to some value by the time you set, rather than change the temp at that time.
Those should not invoke emergency heat.

It is true that a very steep abrupt setback. Just changing the temperature as part of a setpoint schedule might make the energy meter spin.

One or two of the Honeywell Vision Pro stats have a dehumidification option.