Yes, RBAD, I am an old grouch!! Been doing the HVAC thing for 25 years or so and have grown weary of the hype and BS that is rampant. I have an electronic background (braodcast engineer etc.) BEFORE the HVAC gig so am well aware of what goes on in the little box.
You guys asked for the LONG answer so here goes.
Remember, K.I.S.S. as in keep it simple, stupid. A bimetal t-stat is a POS IMHO but they ARE simple. Still better than electronic! A mercury bulb one, Honeywell "door knob" T-87 model is also pretty simple. Millions are in use, most for untold decades. RARELY do anything but what they are intended to do. Anybody can adjust and understand them.
Electronic ones are a bit complex to program. They lose their mind every now and again due to power fluctuations and other demons. Need a battery to "remember". After the novelty wears off, many owners tire of screwing with them. I then get to sell them a NEW HW unit like they had before. Real smart. Spend two hundred bucks to go full circle. Electronics DO have the capability of maintaining a tiny bit narrower temperature range and doing a better job of anticipation. SOMETIME.
The cost to heat or cool your space is based mostly on the "envelope" which is doors, insulation, glass, sun exposure, HOME SIZE, fuel used, fuel cost rate, your lifestyle, weather. Very minor is HVAC unit efficency, temperature maintained, setback/setup.
Setback / setup saves during that period of discomfort, no question. It costs MORE money to return to comfort. If gone for a week and you set heat to 50 degrees, you save. When you "Jack" the thermostat over just a few hours, most savings are lost on the "reheat". In the case of cooling, it may be impossible to cool the space back down at all. If you are stuck with a stinking %#@$$$$$$$&*^ heatpump, a setback t-stat can easily RAISE your bill. Sometimes a LOT. You save during setback when eff. is 200 - 400%. You reheat on strip heat at TWICE up to 4 times the cost!! To a lesser extent, same applies to cooling. AC works best at night and early morning when outside is coolest. That is when you want to cool the space and "store cool" by reducing stored heat in the structure and contents. You want to maintain that accomplishement, not let it be lost so you can cool it back down when outside temps are high and unit works the hardest. Steps on dollars to pick up quarters!!
Most "fancy" T-stats save nothing, but because the owners WANT them to perform "magic" they THINK $$ is being saved.
COIL CLEANING:
VERY important. Often inored. A strong stream from a hose and nozzle works best, aimed STRAIGHT in at 90 degree angle to coil. ALL coil cleaners eat away the fins of your unit. Makes 'em pretty but very destructive if not REALLY well rinsed, at which time they only do SOME damage. Wash coil twice a year from the INSIDE like I do. Opposite the airflow. All that crap is sucked in at 40 MPH or so then cooked at 250 degrees for months. It DOES NOT want to let go!! In general, if you see ANY dirt the thing is filthy. (What hurts you most is the crap between the fins.) I can "lay hands" on the unit tubing and tell you if it is dirty and many other things.
Please note that LONG run times are best. They use LEAST energy if unit is matched to load.
Poor AC performance can be dirty filters, dirty condenser coil, low charge (common), unit poorly matched to load (VERY common), inadequate indoor airflow (almost always) ignorant resident that has closed "some registers" to [save] money (false economy), poor service pratices allowing dirt or moisture into system, plugged refrigerant filter / driers, "low pumper" compressor, among other things.
There is no "magic bullet" to save energy!