Why would it not be possible to maintain a constant rate? You can more than attempt to sustain lag pressure or a constant hand speed you can achieve both.
You could. Or increase the Rate ideally for full power. But the problem is the tendency to see the Rate drop. Its like trying to hold water in your hands. Holding your breath while swimming under water. You can only do it but only for so long.
You can not have a constant rate of acceleration (of the hands) and a constant hand speed at the same time. Lag is sensed at the first lagging component. The club lags the Hands (pp #3 and along the palm of the right hand etc on the downswing, but only the pp#3 attaches to the sweetspot plane so use that one mentally). The Arms Lag the Pivot (pp #1) etc etc.
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