If you use a spline effect, you can avoid choosing knot points by using a natural cubic spline. See the example in this note. Note that if the curve on the log odds scale is as you expect, it might look somewhat different on the event probability scale as in the example. When you say you want to find the point after which "X is no longer beneficial," I assume you mean on the probability scale but are thinking of the log odds curve. So, it would be best to plot both curves to help you be certain of what you want.
Consider the probability curve in the example in the note and suppose you wanted to pick the value where the curve begins to drop. You could use the method shown in the Risk Difference section of the note to estimate the sequential one-unit probability differences. Using the tests or confidence intervals of those differences you could select the point at which the difference becomes significantly negative. In that example, you can see that the change from StartVert=7 to 8 is -0.035 and is the first difference to become significant (p=.038).
