I performed an operation where I selected 3 collinear vertices and scale x=0. Then I performed the loop cut and it worked as desired but when I used merge - at center command, I was not able to perform loop cut correctly. What difference does it make? Ultimately both resulted in same geometry without distorting geometry... see images below. Image below shows vertices on which operation will be performed.
Below image shows loop cut creation after using "merge at center" Below image shows, scale along Y-axis = 0 value and then loop cut was performed and see how it extends upto tip.