Need of reducing problems if we already know that a problem is undecidable
There's a difference between the statements:


There is an undecidable problem.


and


The problem HALT(TM) is undecidable.


For the first one, it sounds like you proved by by showing directly


The problem A(TM) is undecidable.


The point of using a reduction, is that it lets you deduce the undecidability of HALT(TM) from the undecidability of A(TM), as opposed to starting "from scratch".  More generally, reductions let you compare the hardness of different problems to each other, which is a general theme in computability and complexity.