Ok, looks like I have to break this into at lease two parts

Book one

Housing Demand

No: the demand for housing stays the same, thus the amount of money to be had for housing stays the same, and hence if the same number of units exist then the average unit does not change in price by one unit improving. It’s only that this unit moves up within the mass of units, while all the others move down a little.

If you take one home, move it up, then there is one less home in the lower end. Supply in the lower end market decreases.

Average is a factor of adding all prices together then dividing it by the quantity. If one price increases the average increases. If all landowners do this to create profit prices for housing prices increase quite quickly. By making your housing more close to luxury housing you are decreasing the supply of non-luxury housing.

If we have three houses one costs 100 the other 200 the last 300 the average price is 200. If a person buys the 200 house, adds a pool, and sells it for 230 then the average is now 210. The average has increased. Now, if all profit from selling housing was tied to improvement, then all three must sell improve then sell for 30 more. Increasing the average by 30.

No, because this stuff all follows from the previous sentence which I NOed too. The sum of a lot of average zero changes is zero. It doesn’t cause contagion to the rest of the market.

I don't think you understand. If someone buys a house for 100, does nothing, and attempts sells it for 130 they gain the same profit as a person who buys at 100, adds a pool, then sells for 135 (The pool cost 5 to add). In both situations a person profits 30 but in the second, they need money outright for the pool and labour, and the hope that there's a market for housing with a pool when this is finished. In the first, they need only maintain the house.

If everyone simply increases price while doing nothing to improve then the new price for housing is 130. Those who don't increase will have the houses they sell bought by the people willing to do so who will have more money to buy more houses out-competing. People will still buy houses because shelter is a nessesity. This is an inelastic good.

In the situation where pricing increases without improvement, yes, improvement can elevate the class of the house and maybe they sell it for 160 but in a system where improvement is needed for profit their improvement is not special it is market average, and they will profit the same as everyone else. Improvement adds risk, takes time, and at scale will always be beaten by non-improvement.

Lastly, though supply may fluctuate demand at the lower end will be the same. Everyone needs housing. If everyone makes improves their housing to sell for a profit, lower end housing supply decreases, prices rise. If nobody improves their housing and increases lower end pricing people will simply pay more for the required good.