AU has their own store for Android too, and they strongarm new customers into subscribing to it (free for one day, or pay a ¥3150 cancelation fee if you cancel before your first 24h into your contract; after that it's ¥399/month for a selection of apps which are mostly aimed at Japanese or available for free on the Play Store, with a few apps which may be tempting to buy separately and not really worth the monthly price) lol.
I think they all realize that the Apple and Google models are stealing control away from them, but they also realize that Android allows them to take some of that back by offering things they can't offer with Apple. So while DoCoMo is playing strong-headed by refusing to cave in to Apple's demands, AU and Softbank are playing both sides, and it's profiting them.
Seems like the only losers here (besides customers? debatable) are the Japanese manufacturers, who have ever-shrinking R&D teams and rising costs and pressure to compete against foreign (Samsung, Apple) or cheaper (ZTE, Huawei, etc) phone manufacturers, whose presence is being felt more and more strongly in Japanese soil and whose phone features are gradually outpacing Japanese ones. I mean any HTC or Samsung or Apple phone is way better in terms of UI consistency than a Fujitsu or Sharp, though less special and not waterproof, rareliy have Osaifu Keitai, etc.
Those last few things are, IMO, what's keeping the Japanese manufacturers alive until they can hopefully compete more significantly. It'll be interesting times ahead