Is it better to buy @ Trend price -40% (= trend*e^-0.5) all at once. Starting the saving plan for X month from than yields you an underperformance for all X. For X = 12 you get an underperformance of e⁻0.4 = 33%
DCA costs performance, but may be necessary to keep your bank happy
You have to keep in mind your derivation of Cut-Off points. Based on past data you selected a "good" cut-off point for lump sum investment. Comparing DCA with this "good" lump sum investment might be kind of recursive and results might be prone to overfitting.
Your conclusion is true for past Data, but i guess you can not expect it to be true in general, at least it was partly false during the last cycle. Even if there some build in safety factor there is still some risk left that an undervaluation of -0.5 will not be reached in the future anymore
(e.g. this Scenario)DCA can be used to spread this risk and be sure that you are at least partly invested to profit "somehow".
Regarding the performace side there might be second perspective...
If you want to invest a fixed amount of money i guess you are right: A price based DCA is likely designed in a way that you dont fall off the grid, therefore you will have some open orders left if everything turnes out as expected and you will "loose" some performance. The benefit on the other hand is, that the strategy is more robust to misjudgment of Cut-Off Points.
Looking Back the last 10y the correct portfolio weighting of BTC would have been 100% or even above. Obviously that was not the strategy from most of us. Choosing a lower weighting results in more confidence in the investment strategy.
You can use DCA in the same manner if you keep your weighting flexible. Choosing a backloaded DCA e.g. with orders down to ln(-1.0) will likely result in less dependency on cut-off points and more robustness and confidence in choosing a "good" entry point. For the investment itself it DCA seems to be improve the strategy. The "underperformance" due to liquidity left over is meanwhile only based on missed profits or untaken opportunities. At least for me i can say that they do not really hurt me as they happen every day.
Therefore the perspective might change with an approach of "flexible weighting".