Current behavior:
When removing a point, it also removes the handle positions.
Wanted behavior:
Keep the Handle position when removing a point
OR
Joining two points to one while keeping the handle positions
(Basically the same behavior just in different words)
2 minutes video:
https://www.loom.com/share/93cc4590afe54067bb422e54106d3a6a
Important note: This happens when designing in Cubic mode
We have further improved the way FontCreator tries to keep a curve while deleting points. To trigger this, you will need to select a point and then press Backspace. To delete points the old way, just press Delete. It should work with both quadratic and cubic bezier curves.
FontCreator 14.0.0.2859 (64-bit)
Let us know your results.
Much better!!! Thank you! 
Magician
I tried both backspace + delete. Both are useful in different cases.