We don't do detailed estimates, but we do some estimation. Often the discussion around the estimation leads to a change in the task, which drastically impacts the estimate.

That is, by thinking about how to solve it, in order to estimate time taken, one can come up with alternatives which might achieve the same or a similar goal with less work involved.

Maybe the customer doesn't need such a bespoke solution after all? Maybe we can ask the customer if a slightly different solution is suitable?

For example, recently a customer asked if we could make a new web API that they could query for some data. While estimating the point was brought up that just transmitting a xml/json file with the data once a day might be just as good and less error prone for the customer. After all the underlying data doesn't change more than once a day anyway.

So we ask the customer and once they think about it they agree it's a better solution all around. So they get what they wanted for a much lower cost, and we didn't have to commit a lot of resources to make a new API.