There's nothing about the Chrombook Pixel that is eating any of Apple's pie. The only thing it has going for it is a 12" hi-DPI touch enabled screen. Other than that the thing is useless thanks to ChromeOS. ChromeOS doesn't even begin to approach the flexibility and functionality of Android or iOS, much less full fledged desktop OSs.
I don't see a 13" iPad making any sense at all in the current state of the computing world. It's going to be a 'tweener size that's not quite a tablet and not quite a laptop. Too big and heavy to be used like a tablet. Too limited in functionality to be used like a laptop. Now, I could be wrong and it could very well find a niche market like phablets did, but I just don't see it.
A bigger iPad wouldn't necessarily be more powerful either, as the name iPad suggests it will still be a tablet device powered by an ARM-based processor and iOS.
A larger tablet doesn't make sense as something you use mostly on your desk but have the ability to take somewhere when you need to. That product already exists, and it's called a laptop. And laptops come with full fledged desktop operating systems that are infinitely more productive and powerful.
I don't think Apple is convinced this sort of tablet/laptop hybrid device is something the public wants. The Surface Pro is something that embodies this concept exactly...full desktop Windows 8 environment for use like a normal laptop, with the Metro UI that works great in tablet mode. Yet sales have floundered. Many many other convertible/hybrid/detachable keyboard laptop/tablet type devices, yet I don't see many of them taking off in the market. Not to mention Apple would need an iOS/OS X hybrid because iOS is too restrictive to use in a desktop-based device, and OS X is not touch friendly.
Yes, maybe you are right you don't see the need for a device like this right now. Nobody saw a need for an iPad back then anyways. People mocked it for being a giant iPod Touch but still bought it. Apple just create markets rather than respond to what the market wants. Consumers don't even know what they even want if they haven't seen it. Apple desperately need a new growth engine. Their existing ones are pretty much matured. I don't think it is just Apple that need a new growth engine, the entire tech industry needs a new growth engine. There hadn't been much innovation since the high growth phases back in 2010. Well somebody has to make the right bold moves and win it, or we will be stuck with useless chromebooks.
It is quite obvious that for tech companies to market to non-tech users, they really have to market something that will arouse these non-tech users' interests. The non-tech users have absolutely no idea what they will need. It is not like other industries where people can demand what they want, for instance, food companies cater to what food people like to eat, be it chinese, italian, steaks, burgers etc. The point is majority of the people do not even know what computer/weird device they want in the first place. Nobody can demand something they haven't even seen before. Just like how the cell phones used to be plain phones with nothing extra, people were happy with those at that time. Then companies added things like cameras because they want more growth, or just because they can, and people bought camera phones in droves. Did the majority of the people back then demand a phone that can browse the internet, or listen to music, or use apps? No, they didn't even know a phone can be used for things other than being a phone.
It works in similar ways with the "next big thing", I can assure you Samsung's "Next Big thing is already here" ads are not the next big thing. Nobody knows what the next big thing is, even the companies that make them cannot tell. They just execute by putting well designed products out. They won't know which product will stick and which will not. It is just a probability game where you put in your capital to do R&D in hopes to lower your failure rate, and hence increase your returns. It can be seen as a gamble, but talented companies can increase the success probability and lower failure rates.
There are still no user friendly products out there today that sit between the laptop and the tablet. It is that thing in the middle where companies are researching intensely. When that one thing that sits right there in between becomes available, I think we could see a very rapid growth from companies that can benefit from the next trend.