The problem for transpilation has nothing specifically to do with deprecations or constructors per se.
Overloaded constructors and/or methods can be equally problematic for the transpilation but only in some cases. It boils down to that in _javascript_ overloading can only be implemented using runtime introspection of the actual passed parameter(s).
For example createMultiPoint in GeometryFactory has this problem, specifically the two versions that takes Coordinate[] and Point[] respectively. The type of array is erased in transpilation and the array might also be empty so there is no good way to introspect the parameter in runtime.
A similar case is when null values are valid input for overloaded parameters which is why I have, for the JTS fork used for transpilation, introduced parameterless versions of the create* methods in GeometryFactory to create empty geometries and changed calls to for example createPoint(null) to createPoint() throughout the JTS source.
So, you are right that it will not be necessary to remove all deprecations and I'll be glad to work on a PR with the removals I'd like to see for the benefit of transpilation and hopefully follow that up with additional PRs that will make my fork obsolete.