Given the market over the past 100 years, that seems like a fairly reasonable assumption?

Depends if parent means a single stock (like the one given as salary) or a more diversified portfolio. While on aggregate the stock market had a rather stable growth, this is not the case of individual assets.

It isn't going to go up every decade. Also Check markets in Japan and Europe which have been flat 30, 20 years.

That’s because GDP is very tied to population growth, which essentially stoped in Japan and the EU. It still happens in the US due to immigration, but once that stops, then we will stall out as well.

Maybe but the link between GDP and stock market isn't strong either.