From Adobe's point of view the page number is just a string that has
nothing to do with the page number itself. And so is the index. Adobe
has no information at all that the thing on the first page is an index
and thus won't update it.

You also cannot expect from Adobe to support editing equations.

You would need to convince your clients to use something similar to
LyX (and convince TeX developers to write a better LyX) in order to do
that.