For me, many of the reasons set forth above, and here are a couple more for why I want elite status on both AA and BA:
BA gives discounted mileage for discounted fares; no, I don't want just a fraction of the miles I fly on an AA transcon, thank you.
While my BA gold card MAY entitle me to secure an exit row seat in advance on AA, without AA status I'm going to have to call AA (and on the regular line!) and, after a half hour wait to talk to a live person, ask; with status, I can just secure it on line.
You are just going to be treated better by an airline as one of its, rather than its partners', elite corps; I got nothing from LH as a UA 1K when I had a seating problem; I've sometimes been treated well by UA as a 1K when I had a seating problem. I've had great treatment from BA as a Gold, which I don't think I would have had as a OneWorld Emerald, and I've had kindnesses from AA as a Platinum I don't think I would have had as a OneWorld import. This can also be particularly important in the case of irregular ops.