I’d replace the post.
The foam might work for a hot minute but I’m not even convinced of that. I’d think the stress from the weight of the gate will cause it to fail rather quickly.
If the hollow is up in an area where the hinges attach you might split the post with the foam expanding as it cures.
Overvaluing really isn’t an issue causing the housing crisis.
It is more supply and demand as the real cause. when interest rates were low, investors got involved in buying up homes leading to property values rising even more.
From a property tax perspective there’s so many variables that contribute to the value of a house that assessment values are based more on average of a neighborhood area instead of on a house by house basis. Unless the house is sold.
A houses true value is really only known when a sale occurs in the vast majority of cases as the true value is what someone else is willing to pay.
The last home we lived in was 1200 sqft and assessed at 135k if I remember correctly. We sold at around 230k when our neighborhood caught up to rising property values in the city. New owners stayed for a year adding only a privacy fence and sold for 330k.
While I think those sale prices are insane, someone else saw the value and agreed to the price.