Well my first two questions would be
1. With the heatpump running at 0 outside, is it keeping the house warm?
2. If it does keep the house warm, are the heat strips ALSO coming on to assist?
IF you dont know the answer to 2, you need to find out. IF the air coming out of the vents is really warm, like 95-100 I would assume they are. But you can either put an amp clamp on the leads to the strips, or just shut that breaker off for a bit and see if the temp in the house starts dropping (heat pump alone cant keep up).
There is a science to heating and heatpumps and when to switch them on/off and from my research and experience, isnt agreed upon through out the trade.
A 16 seer unit should have no trouble getting to a 3 COP on a 30-40 degree day. That is Cost Of Performance. Electricity creates 3414 BTU for every Kw of power. A COP of 3 means that for every 1Kw your heat pump uses, you should get ~10,000Btu out. But since a heatpump's performance is based on outside temp, the colder it gets, the lower the COP. Until a point at which the COP would be 1, it is more efficient (cheaper per BTU) to run the heatpump as much as you can. Even if it cannot keep up.
Example. Lets say your heating requirement at 20 degrees is 30,000BTU. Adn the COP of the heatpump at that temp is 2.0, and the HP can only make 20,000BTU. Well, thats not enough, and the AUX heat will come on from time to time. But it will still be more efficient than running on ALL AUX heat, cause your first 20,000Btu only requires 1/2 the kw to make than if you were running on 100% AUX heat.
The trouble is, no HVACcompany that I am aware of actually takes the time to set the unit up so it operates at its most efficient. Cause this takes time. You have to monitor the performance of the HP, at various outside temps, know how often it has to defrost (wasted kwh), you have to know your blower CFM, and temp changes from return to supply, and you have to know the kw used by the heatpump. All of that plugged into a formula (or spreadsheet) to see how many BTU the heatpump is capable of producing at varoius outdoor temps.
No 2 systems are the same. It is unique to each setup, and the goal is to find the point at which you are putting more kwh into the HP than the heat you are getting out. And that is the point at which the outdoor unit needs to shut off and run on nothing but AUX heat.
To give you an idea, my 15 year old 10seer HP, that point was 17 degrees vs propane AUX. Since propane is cheaper than electric per BTU, that number would have been lower if I had strips. While 0 degrees sounds low, it may be quite possible that it is still producing heat cheaper than 100% AUX. But when you get that cold, you are also wasting alot going into defrost mode which all has to be accounted for.
The other issue is comfort. Alot of people just dont like 78 or 80 degree air coming out of the vents. Their perception is that it is cold air, even though it isnt. So alot of heat pumps are set to shut off at a higher temp just to prevent return trips because customers thing it isnt working.
If you dont like the HP running at 0, most have a way to adjust. Either a thermostat on the unit outdoors, or on the thermostat inside. You can dial it in to your liking. But if it were mine, I'd be figuring out the BTU output vs KwH input at the various temps and adjust accordingly.