Just to be clear, this doesn't actually set the value of the field B to the value of field A…it sets the value of field B to a reference to the value of field A. This is exactly how it works in a spreadsheet too, so that's probably what you're looking for. There are also ways to create an action that will permanently set the value of field B instead if that's more useful.
And one proviso, because this does a transclusion, you won't be able to use the field B as the value of an attribute and have it work as expected. Like suppose field A contained a list of tiddlers and you wanted to display them; you might try:
<$list filter={{!!fieldB}}>...</$list>
If you do that the filter will just get set to the literal text "{{A!!fdx}}" and you won't see anything. (There are ways to get around this, but I've probably said more than you need already.)