If you meant WYE primary, the only reasons I can think of are cost for the power company (3 single bushing pole transformers are cheaper than 3 dual bushing pole transformers), and special phasing requirements.
A WYE primary with a DELTA secondary has feedback problems. If the primary loses a phase, all the WYE-DELTA transformers are now re-powering that phase in reverse. Other loads on that primary circuit that aren't re-powering it are using it, and generally this results in blown primary fuses all over the place. The power company doesn't like that, so where you see a WYE primary it's going to have a WYE secondary, generally.
Perhaps you meant to ask about WYE secondary. The points you mention would apply to the secondary. It is generally safer because the voltage relative to ground is lower. A 480Y/277 system can supply power to 480 volt delta loads, while only having 277 volts relative to ground (which often gets used for lighting circuits in industrial or large commercial locations). A 208Y/120 system is a compromise; it underpowers 240 volt delta loads, but it does have 120 volt circuits in balance over three phases (suitable for very large services that don't have much need for three phase or can transform or adapt as needed). A 240/120 volt delta system is more suited for many three phase loads and not too many 120 volt single phase loads, but one of the wires is 208 volts to ground.
In Europe and other places, the 400Y/230 system fits well for both single phase and three phase needs because they don't have legacy loads with 2x voltage ratios from Edison style 3-wire single phase circuits. Delta secondaries are rare in Europe.