I don't think there would be much benefit: there are just 2 instructions that can use i: ld a, i and ld i, a. Both are 2 bytes and 9 cycles. That is cheaper than the 3 byte 19 cycles ld d(ix), r, but more expensive than the 1 byte 4 cycles ld r, r'. And the stack can be used as an operand to addition, etc: we have add a, d(ix), etc instructions.
So the register i would only be useful in a very specific situation: i not needed for interrupt mode, an 8 bit location is needed to hold a result currently in a that next will be needed in a again (but in between a is needed for other uses).
So while there is a situation where such use of i would provide a benefit, IMO there are lots of more important things to be done first.

 
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