None of the calculators have an input field for incurred heat loss while you're stirring with the lid off. I tend to lose 2-3 degrees F each time I open the (rectangular) cooler and stir for 1 minute. That's indoors with a 5.5 gallons batch of 1.060-1.070 and a water/grain ratio of 1.5. In cold or breezy weather that loss would be higher.
For the same reasons, when mashing in I need to add 6F (!) to my calculated strike water temp to compensate due to the longer stirring period with the lid off.
I also lay a double sheet of heavy duty aluminum foil right on top of the mash before closing the lid, to reduce heat loss to the headspace.
Now the need for a mashout depends on many factors. If you want highly fermentable wort, a mashout is not needed, or even recommended. The longer time the enzymes are active the better. If you want to reduce fermentability, a mashout is only needed if your lauter is slow, you can't start heating the (first) runnings right away or it takes a significant time to reach 170F (large volume, slow burner, etc.).
If I want to do (serious) step mashes I mash in the kettle over direct but low heat (induction plate, tri-ply bottom kettle) and constant stirring while heating. After a final 10' mashout at 168-170F I dump the whole lot into the cooler mash tun for lautering and sparging.