I struggle to leave the house sometimes; I suffer from anxiety as well as complex PTSD. In a way, I was like your DW in that I was very reluctant to ask for help. This was mainly because I didn't want SS involved; we were already on their radar as our DDs are adopted and we were looking for help with DD1, who is SN.
But I actually made myself do the things I needed to do, like the school run and shopping. I also had no problem with my DH taking the DDs out. Although, in contrast to your DW, I really love being on my own, with my 4 cats for company, which has a lot to do with the fact that DD1's meltdowns are exhausting.
When you've had long-term MH issues, you develop a sense of hopelessness, you think that nothing will work so what's the point?
In my case, I went on anti-depressants and I'm on the waiting list for EMDR. I'm doing what I can as I want to be the best mum I can be, I don't want to short-change my DDs, or my DH. I don't want my problems to impact on them.
Your DW's issues are very real. But she nevertheless has to take responsibility for what she's put you and your DC through., and do what she can to put it right.
You've been really patient with her, but it is time for you to say to her that you won't put up with this anymore. And yes, if she still refuses to get help, I think you should leave, and with a clear conscience.
Good luck.