Why is a transformer necessary?

A transformer is not 'necessary'. The human race evolved, and developed

cultures, societies, disease resistance, and technology, without ever

seeing a transformer.

But there are specific situations in which desirable things can be accomplished

much more effectively and efficiently with a transformer than with any other

device or method. Here are a couple of examples:

-- If the voltage you have available is not the voltage you need, then you can

use a transformer to make the change. (But that only works for AC.)

-- You can use a transformer to change the output impedance of an amplifier

to the impedance of the speaker or earbuds you want to use with it.