Doubt it they take some killing. They were very popular in the 70'/80's and I was surrounded by them.
Dont generally need to prune/cut them back just keep tidy, but the time to remove brown/dead material, especially from the centre, is January and February before the new shoots form and they should start to appear in May. I know on mature plants that some burn the centre to promote new growth? but I have never seen this done.

If your wife has been cutting them back every year in Spring, that's exactly the right thing to do. Its possible she hasn't cut them back hard enough, in fact - they should either be hacked right back to the central stump, all the spent flower stems clipped as low as possible, and then the top of the stump raked out, hard, to remove any debris and dead material, or can be set on fire.
It sounds as if the centre of the plant has collected a lot of dead material, which means you're only seeing growth on the outside. If you're able to set fire to it, do it in spring - if not, a very draconian cut back and very severe raking out of the centre might suffice.
These plants grow in places where bush fires are common - they respond very well to hard cutting or burning, rising anew from the ashes.

Get rid of your pampas grass completely by burning or spraying repeatedly with glyphosate.
Instead, plant Miscantus giganteus. Not only is this a perennial grass far easier to control than Pampas but it is more decorative, can be used as a supply of 'bamboo' canes, and looks good in winter as well as spring and summer.
No contest!

No contest indeed - I'd choose pampas over miscanthus any day, different effect and plants.