Why We Run Motor in Delta Not in Star Connection

Because you get only 1/3 of the motor's rated torque and hp if you leave it in star.

You could also ask why not start in delta configuration then you might find the answer to your original question.

(1) you can't because the timer in star-delta starter will put motor in delta after settee time. (2) you may continue motor in star provided your load requirement is less. In this case you are un-necessarily selected higher rated motor. Commercially wrong decision. Instead you can have delta connected lower rated motor on DOL starter. Hope this satisfies your query...