In OP's example, any more implies [this] was important [for younger generations?] in the past, but it no longer is.

The opposite of which is that it never was important before, but will/may be in the future...

[This] is not important for the younger generation as yet.

In OP's example, any more implies [this] was important [for younger generations?] in the past, but it no longer is.

The opposite of which is that it never was important before (but will/may be in the future)...

[This] is not important for the younger generation as yet.

I can't exactly put my finger on why, but I feel OP's use of any more is somewhat "clunky" regardless of whether it's coupled with not important or unimportant. I would say...

[This] is no longer important for the younger generation.