"If your switching earlies and lates it means you have to completely readjust your sleeping cycle every week, isn't it so? Hence I was wondering why they just don't have pilots do one or the other."
Not really. You are pretty much always asleep when it matters i.e. between 0100 and 0400.
Also in some bases they only operate long flights on earlies and short flights on lates, this would mean you would be less productive for the company but most importantly earn less.
If you were flying long haul then you would experience true disruption of your flight pattern. Here you are in your own bed every night and generally well rested.