I get what you're saying but I wouldn't personally call zeropage bytes _registers_, even though they are physically connected to internal ones. I treat them as a special zone of memory that has special properties. There are many of these things and just like you would start with any of the old machines you'd first take a look at the memory map to see where's what and how to use it. Registers in a traditional sense would be those few mentioned of which you'd only ever really touch A, X, and Y.
One reason to consider them equivalent to registers is that the cycle time for zero page and register-based instructions is the same (2-3 cycles). The full 16-bit instructions ("absolute") take at least 1 extra cycle and often 2 if crossing a page.
Of course there is the Atari 2600 where you only have 128 of those bytes with RAM (80-FF) and the stack is set to page 0 instead of 1 (not that you'll use the stack a lot in an Atari 2600 program).
you're right, I meant $0000 and $0001 which _are_ registers. The rest 254, yeah. Zeropage is a must on C64 at least. I don't know much about other platforms.
So 0 and 1 are connected to the 6510 I/O data direction and I/O data register, but there is still RAM there too. Seems the 6510 won't issue write signals to the bus for addresses 0 and 1, but the VIC can see them and it's readable through sprite collisions.