I think one should write testable code,past a certain "size" because somebody sometimes will have to maintain that stuff.

the question is should it be "unit testable" or is it ok just to write integration test.

I think the code you write should be unit testable,doesnt mean the units cant depend of apis you didnt write(while already tested).

should you expose everything for the sake of being able to mock stuffs up?

I'm dont know the answer. to that question.