It could be argued about why estimates are needed to be prepared at the beginning of the cycle, but there can be many reasons for that. One of the biggest reasons was about wanting to have a good idea about the number of features that would be possible to be done in the given cycle. This is necessary for the team, and this is very important for the stakeholders and sponsors of the team. In a number of cases, the plan for the release will not be approved until there is an assurance that a Minimum Viable Product has not been planned. Given that the release of a product can have profound implications on the financial status of an organization, it can be very important to do planning about the number of features that can be fit into the release.
Doing this estimation also allows the team to do the required resource planning, and even though the number of resources may not change too much between releases, if there is a need to do a big bang release, then the team would want to know the number of extra resources that are required for this release. So, let us work with the assumption that the team needs to do the initial estimation for the features that are planned for the release.
Now, the biggest problem that occurs is that when the work for a release is being estimated, the people doing the estimation are the more senior developers in the team. Typically, the estimation exercise can only last for around 5-10% of the total time of the release, and it is really not possible to do the logical task of breaking down the features into detail deep enough that the estimate would be very accurate. So, a lesser number of people are drafted in to do this kind of work, and an equal assumption is that the estimation is primarily done by the person using their previous experience to determine the scope of work for the details of the feature and using this for the future.
But when it comes to doing the actual development work for the feature, you cannot have these senior people doing all the work. The work is shared among the team members and this is where discrepancies come in. You can have the senior person being very skilled in doing such work, but the person who is actually doing this work is not so skilled and you end up with more effort required for doing this work. So, whenever the work allocation is being done, there is a need to map the estimate with the person who did the estimate, and the person who is actually going to be doing the work. A skilled manager who knows both these people would be able to do this to a large extent and be pretty accurate in this. At the same time, the project manager should continue to track and compare the effort discrepancy mentioned by the engineering manager with the actual effort discrepancy.