Interpolate vertex attributes with $z$ AFTER homogeneous divide
The $Z$ of NDC space is related to $1/Z_\text{view}$ but not the same. With a typical projection matrix,  they're related by an affine remapping,
$$
Z_\text{NDC} = a \, \frac{1}{Z_\text{view}} + b
$$
where $a, b$ are some constants related to the near and far planes. So, in general you wouldn't be able to substitute $Z_\text{NDC}$ for $1/Z_\text{view}$ in the interpolation expressions. The $a$ factor isn't a problem, as it would factor out and cancel, but if $b \neq 0$ then it will produce some extra terms and throw off the interpolation.
If I'm hearing you right, it sounds like you're concerned about the idea of needing to prepare every single vertex attribute value (multiplying by $1/Z_\text{view}$) before interpolation and then reverse that afterward. Well, there is an easier way: we can create perspective-corrected barycentric coordinates $w'_0, w'_1, w'_2$, defined by
$$
w'_i \equiv \frac{w_i / Z_i}{w_0/Z_0 + w_1/Z_1 + w_2/Z_2}
$$
Then we can interpolate any attributes by $w'_0 A_0 + w'_1 A_1 + w'_2 A_2$, and it will be perspective-correct interpolation. You can verify this is equivalent to your original interpolation formula in your question. If we have more than three scalar attributes to interpolate (which we usually do), this would be the cheaper way to do it.