A '816 would indeed be much better suited to access 512K of banked memory rather than banking through an 8K window but perhaps they don't think 65816 counts as retro enough, or maybe they're just masochists
With sharing I mean, when you have two or more tasks of which only one instance will run, they can use the same direct page. Similar if you can statically limit the stack size of the tasks to a fraction of 256 bytes, you can fit multiple stacks on the same page with some work.
Program counter is 16 bit, with a separate bank byte; it'll wrap when it hits the bank boundary.
Constantly having to flip between register modes is a hassle. And makes it very difficult to write compilers and high level languages. Many common patterns require flipping back and forth a few times.
Either they needed to have a whole new set of addressing modes, or they should have just added 3 new registers -- 16 bit versions of X Y and A -- and let the two co-exist.
Honestly, this is an era when a 68000 could be had with a full 16 register set of 32-bit registers. The 65816 doesn't look so hot in that light, though it certainly was faster at interrupt handling.
I guess Nintendo made do with their modified 816, but it really is not a nice architecture.