Since you cannot achieve the code required 75 mm of cover to the rebar for concrete poured against soil, you cannot put rebar in a 4" thick slab and be in compliance with the intent of the Code unless you use stainless steel bars, which seems going rather overboard for a house.
A 4" unreinforced slab on grade that is not acting to support structural members above, should work fine if there is a proper compacted granular base, a competent native undisturbed soil with no soft areas, that has been inspected and approved by a geotechnical engineer, no water problem or uplift, not some very unusually heavy concentrated load, and the concrete mix is properly proportioned without too much water.
If the forgoing conditions are not met, then you are kidding yourself if you think rebar will make it ok. Keep in mind that all concrete cracks due to shrinkage, irrespective of whether it is reinforced or not.
A disadvantage of the rebar is that if you ever have to break thru the slab to get at leaking underground drain piping, as I have has to do, it will be more costly to do so because they will have to cut the rebar. I would not put rebar in, not because of the cost, but because it will be of only marginal benefit and will not meet Code for required cover, if the slab is 4".