Sorry for the confusion. I mean the well is 5 inches, meaning that currently the pump/motor is surrounded by a 5-inch well casing, rather than open water. I agree that 4-inch flow inducer sleeve will increase the water flow downside, but the increase may not be significant compared to the current 5 inch well casing.
In the video comments, people questioned: (1) the sleeve pipe (4in SDR35 pipe sleeving a 3.75in OD pump) is too small. It restricts the intake. The sleeve should be large, such 6in. It is not practical in my case because my well is 5in. (2) Cutting and clamping the top of the sleeve to improvise a collar is asking for a future disaster. (3) The grub bolts at the bottom are another worry on a flailing pump.
In the first link in post #23, you calculated the annular space showing there is enough space between the motor and the pipe. Thank you for your explanation. In that post, the person asked for the pump in a lake, rather than a well.
"Using a submersible pump in a large tank or large casing, I understand the need to force a certain amount of water flow past the motor for proper cooling."
In that case, i.e., open water, I definitely agree with you that an inducer sleeve is necessary.