Well if you haven't already heard it a thousand times,
we know pursuing (chasing, "fighting for the marriage", etc.) just doesn't work.

She expects you to do this,
for many different reasons I'm sure,
one of them possibly to satisfy her ego, it's hard to say.

You became someone she cheated on a few years ago, you became someone she stopped caring for in the right way, you became someone she didn't want to be with anymore and originally wanted to kick you out of the home when this nonsense started - fighting for someone who would do those things to you doesn't make sense to me and hopefully it doesn't make sense to any LBS struggling with this.

The fact that she asked you that indicates that letting the WAS go works, she expected you to chase her, pursue her so that she could continue "running away", when you stop pursuing a WAS, they don't have anything to run away from, in fact, it causes them to start asking themselves questions, one of them being "why didn't you fight for me?", she changes direction, she stops keeping distance from you when she originally wanted a lot of distance between the two of you. The WAS contacts their LBS, texting, calling, emailing, leaving voicemails, asking for favors and assistance with tasks that you have confirmed could have been easily done by her alone. They are all excuses to get into contact with you, even if they don't believe this fact to be true even to themselves, there is no other way to explain it.

You don't need to "wooo" her, quite the opposite, you need to let her pursue you, you need to let her believe that you have finally understood and agreed with her that you believe it's over, you won't fight for her, you won't chase her anymore, you've given up on this relationship and are moving on with your life. It's only when this happens that the momentum of this situation moves in your direction.

Don't be surprised of some new developments in your situation (with regards to your wife's actions towards you), they could happen any time (and then again nothing may happen), either way like you said, you are embracing being on your own and you feel less stress, anger and tension - that's a small victory right there ;-)