Immigration officers are primarily in the job of inspecting the traveler, not the passport. Watch any documentary about customs/immigration, and this is a recurring theme. When they take their time riffling through the pages, they are sizing you up more than they are really taking any interest in the stamps. If you give them a blank passport, they will often answer it with an equally blank stare that goes on for 30 seconds - again, sizing you up.
It's not that the stamps are of no interest, and at certain ports (e.g. Israel) the presence of certain stamps in your passport can become a real problem. But in general, at most ports the stamp review is a secondary task to their primary task of evaluating the risk posed by the traveler.
So I would consider the question from another angle: will renewing to get an empty passport guarantee reduction of my time in immigration in any way?
The immigrations officer will still take time to consider you. And the length of that time is entirely at his/her discretion.
Moreover, there could still be long lines at customs. Or an immigrations officer could still decide you look a little too much like someone on their watch list and pull you aside for more intense questioning. Or your electric toothbrush could have started itself up inside your checked bag, leading to a tense and lengthy discussion with a baggage officer before you finally convince them to open the bag and let you move on. The passport review is a tiny part of the time cost of customs.
For example, JFK Terminal 4 has a daily peak average wait time of 83 minutes. Even if you reduce your time at the booth from 3 minutes to 1 minute, you are effectively trying to optimize to save ~1% of the time you will be there from entry to the customs hall to final exit.
Not worth it. Just travel normally and renew your passport on schedule. Customs is just that: customary practices. Embrace the local custom and enjoy the journey - a maxim that applies equally well to ports of arrival and to travel in general.