This is the type of question that, to my mind, gives rise to lots of related questions that, perhaps, don't appear obvious to the o.p. - but do to me given the differences in climate zones we're both in.
Here concrete cracks...and we build basements and deal with temperature extremes too.
I'll start by hypothesizing that in Kentucky as opposed to up here, you may (or may not) have a crawlspace or a basement underneath your kitchen slab, meaning that the slab is off the ground...seems unlikely, but I don't really know how things are done there. I'll also suggest it may be right on the ground and that the op may (or may not) know how that slab was 'waterproofed' from underneath...was there any attempt made to keep the flow of moisture through the slab somehow under control...the answer to that goes to the cracking issue.
And I'll also throw out this concept: that concrete slabs are 'breathing' systems where moisture and air go in and out at a rate that depends on a number of other factors, and is driven by hydrostatic and vapour pressure both from above and below and that cracks may appear due to a change in one or both of these external physical phenomena (air and vapour transmission). I don't know; I'm wondering out loud -or typing out loud, actually.
Furthermore, if you change
those rates of transmission by covering the top or bottom surface of a slab with a different flooring, i.e. change those rates of transmission, would that affect the cracking issue? wouldn't there be more or less vapour transmission through the slab
and is it not possible that cracks may appear as a result?
IMO, either way, Ditra is a sound choice...