[MOVED FROM FEATURES REQUEST TO BUGS REPORTS]
Usually when you edit contact you do this to add some detail for example birthday or email address.
Open People app → Tap on contact to see details → Choose Edit from pulley menu
When you do that keyboard is open and cursor is in Name field.
Usually people wants to add some details not change name, open keyboard covers fields you want to add.
It will be easier to add some detail if edit site will open with closed keyboard.