Won’t it make more sense to stick to your delivery promise than sharing a tracking number. If you are trying to say that I shipped your product but its up to the delivery guys to meet the promise, I am like “duh.”
If your email with my tracking number is to show how genuine or professional you are, please note that I placed an order with you because I thought you already met the above criteria.
Side Note: I am sure there is a history for the evolution of sharing a tracking number. For a customer, he would rather have his product than a alpha-numeric code in his Inbox.