You are very much correct. Running the BBK and deleting the pump is very advisable for maximum power. However, when running the BBK and keeping the stock carb, I advise to keep the pump. The reason being, is that the stock carb needs all the help it can get. Burdening it with having to supply oil as well as gas to the engine could be more detrimental then risking a pump failure.
For the most part, Honda makes an excellent pump, and the chances that it will fail are very slim. Removing the pump and running straight premix is great for peace of mind and over all HP, but what you lose by deleting it, is fuel delivery. If you go with an aftermarket carb, this is not an issue at all, and in fact is highly advisable. But when you are dealing with the stock carb, you wanna keep everything else that makes the engine run as stock as possible for maximum power.
The more gas you allow the carb to deliver on a stock carb, the better off you will be. An oil pump ensures that you are letting the maximum fuel the carb can put out on an already weak carb system, gets delivered into the piston chamber. Whichever one decides... keep the pump or ditch the pump, DO NOT
try running the BBK with straight gas in the tank, you will burn up that piston real quick!!
Here is a video showing and explaining what happens when you let the carb give all it has to give while using a stock intake, which is very restricted. In this video, the BBK was ran with the stock carb and intake using the standard jet (#90) supplied with a BBK, on a Dynojet 250i. The carb was allowed to run free air with no filter so as to allow the maximum amount of air in that it could handle. As you will see in the video, analysis showed the INTAKE is what is holding the BBK back, not the carb or air coming in. Your stoich AIR/FUEL ratio, which should ideally be in the 12's, is stuck hanging in the high 13's and low 14's.
Because of a weak intake system, you get a bottleneck after the venturi where the Spree wants to breathe in more of the air/fuel mix, but can't. This is why a performance intake is very vital.https://www.youtube.com/watch?v=GIVuMWGCNm4
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