That’s one way of looking at it. The other way is: imagine how much your client is going to trust you forevermore if you tell them you did it in half the origi

That’s one way of looking at it. The other way is: imagine how much your client is going to trust you forevermore if you tell them you did it in half the original estimate. The next time you slip they will happily pay you because they know you are honest. They might like you so much that they will do referral calls for other clients. Etc. Reputation matters.