dear shahid bhai
car washing / drying process are most critical steps in whole car detailing process as most of swirls and light secratches happen to appear in these steps due to wrong method and inappropriate products use.
main aim of weekly car washes is to keep clean car skin from dust, tree spa, brid droppings, brake dust etc and lubricate the car skin so they do not secratch the paint while washing and drying process.
dish detergents are not good / safe option for this purpose as they specialy designed with stronger chemicals / agents to clean the left over "sallans" from our dishes, means they having de-grezer/ de-waxng agents in them, use of these products make the car skin dry means swrils and secratches while washing and drying process and after some time dull the paint and remove the protecting coatings, also cause rust etc
on other hand speciallized pupose built car shampoos not only give good cleaning but also provide enough lubricants to paint which help to rinse away all said particulars harmlessly from paint, having balanced ph values etc
what i observe we give most attention to expncive finishing waxes while ignore most critical part in whole detailing which is washing/drying with right technique / right products in this way we can keep our car skins swirl free for comparitivly longer time means will save our extra efforts / money for car compounding and polishing etc 
in my humble view we should not use detergents for car wash , infact a lower quality car shampoo like formulla 1 far far better than these detergents and sure good brands shampoos best options with extra care to car skins