Housing is fungible. If you produce luxury housing, then that reduces pressure on existing upper-mid housing, and reducing pressure on upper-mid housing in turn reduces pressure on lower-mid housing, etc.
Where I live, building affordable housing for low and medium income is at the moment financially unattractive, so it isn't undertaken in the numbers required to meet projected demand. Offering luxury housing for the small segment of the population able to afford it, won't make a difference.
https://www.reuters.com/markets/europe/german-housing-shorta...
https://www.reuters.com/markets/europe/german-home-building-...
To the extent that someone in a less expensive form of housing vacates it to take newly built luxury housing, it seems like the marginal effect from that luxury unit existing is to increase the supply of total housing and of more moderately priced housing by exactly one unit.
(To the extent that new luxury housing exclusively attracts outsiders to migrate into the city who otherwise wouldn't, it doesn't help. I doubt that this exclusivity holds.)
In any event, abundant housing is essential to filtering taking place. If there is scarcity, for example, if there's already a pent up demand for luxury units, then those units can be quickly occupied without anybody vacating the older units, and then the price won't go down. It might even go up if low-cost housing was torn down to make room for the luxury units.
It's like when you target funds in a large organization. Yes, your $100 donation goes to, say, fund program X, but money is fungible and the org can just pull $100 of its general funds out of program X and put it in program Y.
Housing is of course less perfectly fungible than dollars, but at the end of the day almost all units of housing house one (1) household, and that household needed somewhere to go, and using this unit of housing for this household frees up more housing for another household.
One of those (Mast 2019) specifically tracked individual persons to confirm that the mechanism of action is the wealthiest tenants moving into the new building and freeing up units in the slightly-older buildings, where slightly-less wealthy tenants then move in from even older buildings, etc., lowering rents all down the chain.
If the goal is to lower rents down the chain, why not just build more units at every price point? That way everyone, not just the wealthiest, will get new units and not be subjected to old stock in potentially older / worse neighborhoods.
Because zoning prevents that. This is a highly-idealized thought experiment, but imagine a housing market where there's demand for 100 luxury units, 100 cheaper semi-luxury units, 100 still-cheaper middle-class wage earner units, and 100 cheap working-class units. Then imagine that local zoning regulations will only permit 100 new units to be built, and more that that will prompt voter revolt. Which 100 units will be built? Only the luxury ones, obviously. Nobody's going to build cheaper units if it's a mutually-exclusive choice between building cheap ones and the expensive ones.
Zoning is why you only see expensive new housing get built: it restricts how much can be built, so developers respond by only building that which gives them maximum returns. You know how quarterly sprint planning for software takes every feature request, orders them by priority, and then draws a line under how many man-hours worth of work your team can do? Developers do the same thing: they rank development proposals by profitability and then draw a cutoff line under what current zoning will let them do. Loosen these requirements and just let people supply the required demand, and you'll start seeing the units at every price point that you want.