I don't see how decimal-to-binary conversion would have anything to do with the TIA chip. I suspect that it used a polynomial counter instead of a binary integer counter because it used fewer gates and had less delay.
By the way, the CPU, like many others back then, could do addition and subtraction with binary-coded decimals.
To position objects horizontally ideally you would have a register where you load a value between 0 and 160, but instead you have to strobe a register when the CRT beam is near the horizontal position you want, which will be +/- some pixels due to the CPU being 1/3 the clock of the TIA and 6502 instructions consuming 2 to 8 cycles. So then you have to "fine tune" using an additional register to shift it left/right -7 to 8 pixels.
By the way, the CPU, like many others back then, could do addition and subtraction with binary-coded decimals.