I think even a swing of 5 degree in a day is normal. Corals should be fine just the sensitive reefers.like us.
In natural, I believe reef islands do get cooler at night time and hotter during the day. I used to live less than a half mile from reef islands and the ocean do get cooler at night time and very wicked hot during day . (More than 10 Fahrenheit swing)
One reason to allow swings is just to go easier on the components. By rapidly shutting the heater on and off you are giving it lots of opportunities to get stuck or malfunction. I think it's totally fine to allow 1-2 degree temperature swings (and probably more, honestly).
When you have a couple of $1k dollars in corals in your tank, for me is a non-discussion topic not having , at least, a $100 reefkeeper to control the heaters.
As I do not like to have all the eggs in the same basket, my heaters are all controlled by more then 1 reefkeeper ( 1 in the DT and another in the fuge). Moreover, I have more than one heater in each tank (2 at minimum) and each one is underrated for the tank. Also, all of them have their on/off setup 1 degree over the controller max temp setup. In that way you cover many potential errors / malfunctions.
My APEX, concerning temp, is just for the graph. But , I really do not need it for that. You can see how the reefkeeper get the temp with the parameters I set it up. Today I am using my APEX only to control my DOS system. And to check the tank parameters during my travels (like PH, temp and dosing). But this is me. Others will disagree.
It depends on other parameters as well. If your corals are already struggling in the tank due to other parameters, a little bit of temp fluctuation will push it over the edge.
It's very easy to keep the temps stable in the winter time. It's easier to heat water than to cool it. In the winter time, you should be able to control a much tighter fluctuation. For most, it should be within the hysteresis of the controller. In the summer time, it's a total different story. And the amount of temp spike your corals can handle will depend on other parameters as well.
For my tank, winter time +/-0.2degrees. For summer time, +2degrees during the halides period. On a really hot day and if I forgot to turn on the AC, the temps will hit the max +3 degrees in which case the halides will turn off.
If you run your tank normally at 76, a +5 degrees might not be that bad. If you run your tank at 80degrees, a +4 degrees can do some damage. I personally wouldn't look at the absolute change in other people's system. I would keep the tank at the temperature I'm comfortable of keeping it stable and have the +/- window as small as possible.