Perhaps a solution is to distinguish between an estimate and a detailed plan. One is a quick guess with high risk, the other takes time and research to prepare

Perhaps a solution is to distinguish between an estimate and a detailed plan. One is a quick guess with high risk, the other takes time and research to prepare and the risk of running into a delay is lower. And often the best solution is to have none; perhaps part of the problem is that people are often too afraid or have not enough trust to work without plans or estimates when needed.