If you have constantly back to back meetings, you should ask yourself how this is possible. Could you delegate some of these to your team members and would they have the authority to make the decisions? Has the organisation embarked on too many initiatives? Can meetings be shorter and quicker? I won’t go into how to run meetings because that is a subject by itself and I think already much is said about that.
But there must be options to respond to questions and assure you can communicate your decisions to your team members and stakeholders timely.
I once worked with a CIO who, being a busy man, consistently would answer at least the next day any questions you had sent by email. He was an early riser and used his morning time to respond to all his email. Very effective. As a project sponsor, he organised also the steering committee meetings meaning that they would always be held regularly and project progress was assured. Most project sponsors would leave it to the project manager to organise the steering committee. This means that then project manager will need to struggle to find the time in the full agenda of the sponsor with the constant risk that they would be delayed or cancelled.
I also always respond to emails and questions immediately unless I purposely delay it to obtain more information. The issue is that if A asks B who asks C and each person takes 5 days to respond, the whole process is delayed by 10 days. If each person responds within a day, there is only 2 days delay. Delay simply costs money and specifically if A or B are whole teams who also need to produce something following the answer, you can easily see the impact.
Responding immediately will introduce a temporary feeling of being rushed. But these are short bursts. If you wait, you will have a larger backlog while in the mean time you have the constant stress of all this work piling up. Once you then start working on the responses, you might not be able to complete it all. This will further increase stress and rushed feelings. The risk is then that people will make decisions on their own with the risk that work has to be redone.
Much time of managers is spent on fighting fire. This can be reduced by implementing best practices. Once you have improved your processes and practices, I have found that a team can rather well run on its own. As a manager you have done a great job if you can go away for a while and this does not cause any issues. Just like a parent who raises a child, your objective is to make your team stand on its own. Don't make your team depend on you. Effectively it will reduce the number of questions being asked to you, it makes it easier to delegate and it will increase the time you have available to work with your team. This is what I found out by experience.
So if you are an early riser and your calendar is booked out because your are involved in a change program to implement best practices, I predict in any (near) future you will have more time available.