I've always seen estimates as trying to guess the highest number the PO will accept, the time or effort involved in actually completing the task is irrelevant. I have never had a PO or anyone else complain that a task was completed more quickly than expected. However I do have to be careful to not tell them it is complete too early, lest they start expecting shorter cycles.

At least in my company we've stopped calling them "estimates". They are deadlines, which everyone has always treated "estimates" as anyway.

Unfortunately in the real world deadlines are necessary. The customer is not just mad that they didn't get the shiny new thing, especially in the case of B2B stuff, the customer is implementing plans and projects based on the availability of X feature on Y date. Back to the initial point, these deadlines often come down to how quickly the customer is going to be able to implement their end of the solution, if they aren't going to be ready to use the feature for six months there's no reason for us to bust our asses trying to get it out in a week.