Around here building code states that any stringer over 3 steps requires a footing.
They require things they don't understand themselves.
You can also have problems associated with doing concrete footing in the ground also since they don't require the footing to be 12" wide and some places they don't require to go 36" deep depending on the region. When you place concrete footing below frost line it might not help to prevent stairs from heaving, especially some will dig a hole and put the post in the concrete and attach stringers to it.
The top of concrete footing above ground or (or the post itself) provides source for heat transfer from the concrete to the surrounding dirt or air, keep in mind that concrete is a very good conductor of heat and the change from moisture to ice requires that heat transfer.
When you have the ingredients, you get ad-freeze and that is what causing the heave... That is when the moisture in the soil tends to move from areas of higher temperature to areas of lower temperature and when it happens, you end up with is a cylinder of ice which will form around the whole footing column and post (if present). That ice can lift the entire footing and it don't matter if the bottom is bellow frost line.
Luckily in most places frost will not even reach even a 1/4 of the footing depth from above. I remember doing one deck in the middle of the winter and it was fk brutal cold which lasted for weeks, the frost penetration was 12". I was talking to some guy from Mane a while back at the deck show, talking about dealing with this stuff, he said he has building on slabs and his deck stair rest on the slab and with the winters they have he said, everything as it was built yesterday.
IMO you have less chances have stairs heave being on the slab then on the footing. Look at structures like sheds on slabs or on 4x right on the ground, etc including my shed on the slab its been standing there for 12 years now and it nothing got out of whack... my other shed in the old house been there for 11 years with double doors also on the slab, nothing ever heaved and doors never needed adjustment, etc. As long as you have proper drainage, your stairs will not go anywhere being on the slab and you don't have to do s^*t to them to allow movement.
Good luck