Nobody has advocated for a "fancy" T-Stat. The digital stats that have been recommended are all very basic.
It is incorrect that a "too accurate" (actually "too precise") stat will affect running time. All stats have hysteresis built into them, which is what determines minimum run time. This is important, and is rather tricky to do with a mechanical stat, so it sometimes doesn't work very well. In a digital stat, it is very easy to do properly. Sometimes it is even programmable.
Mechanical stats meant for home use are not designed for the constant vibration found in a vehicle. Companies like Atwood make RV-specific stats which are more robust. The problem is that many of them make a loud "ping" every time they go on or off. This used to wake up DW every time the stat went on or off. This was the proximal reason I upgraded to a simple (and silent) electronic stat. It was a very worthwhile upgrade.
I have gone over the thermostat questions in structures quite a few times the most recent about a year ago when I replaced the house heating and cooling system myself, and would tend, in general, with previous post about unwanted, energy wasting, frequent cycling.
Frequent cycling in many or our RV furnaces wastes a lot of electricity power and some propane power in the start/proofing/run process. The hot water systems are probably a bit better, but I don't know that.
AFAIK, the only benefit of frequent cycling is to maintain a more uniform room temperature, and the public has tended to wanting that feature. This is also one of the reasons for the multistage furnaces and AC, I think.
I have not found moderately priced, or cheap, thermostats that have adjustable hysteresis, or whatever name the call it like range, variation, whatever. You get what you get and most don't tell you what it is.
The higher end stuff used to, for the most part, have a settable two or three point hysteresis, but when I did ours this time many did not, including the top end Honeywell units that are very popular. The Honeywells were at +/-.5*F IIRC which makes for very fast cycling. I searched for a long time to find one with settable hysteresis and with the other things I wanted like intelligent recovery logic. I wound up getting an Emerson (which is really the old White Rodgers) commercial unit that had all I wanted. It also used manual switches which are much more intuitive, and hopefully reliable, than the small touchpad ones. DW hates touch pads so that is a plus. Her hate got reinforced big time with new HRV we put in with the new furnace and AC, as it had a horrible touch screen that required a bunch of scrolling to make simple changes, and we had multiple failures due to lockup that required 4 replacements in 18 months before I finally ripped all the electronics out of the unit and made a mechanical relay setup for it. Two switches, 4 LED indicators, mechanical humidistat plus a small thermostat for defrost function. We got more control with ours than than the touchscreen gave and it has run a full year without issue so far.
I think most of the settable thermostats have +/- .5/.75/1.0 degree or so settings of which we use .75* and get a 1.5* variation in room temp. Of the ones I could find out for, most of the digital, newer, version were on the tight side of .5*. We have the furnace and AC sized as low as we can and still cover the loads needed for the house in very hot or very cold weather, so we naturally have longer, more efficient, runs besides.
In our van the furnace is very large for the volume of the space so inherently runs less time, plus as soon as the fan goes off the airflow in the space changes so colder air can easily gravitate to the thermostat and retrigger it early. The original mechanical thermostat does seem to have a wide hysteresis and does a pretty good job of balancing comfort with run time. I haven't even looked to see if it has one of the old school "anticipaters" in it to make it adjustable hysteresis.
I am not sure what we will wind up with if our stat dies, but I will certainly want one with wide hysteresis.
Easy fix with a screw but not something I anticipated
