In practice, "pushes down the prices" is an overstatement, and what actually happens is that once demand pressure reaches a certain point new luxury supply only opens up higher pricing tiers. It potentially stabilizes older construction, which is not bad, but doesn't seem to provide downward pressure. The only thing that seems to do that is non-marginal demand dropping out of the market.

And if you follow it through that's how the incentives seem to be aligned. Capital examining opportunity in construction will want to chase the highest return it can and if you have capital the marginal cost on luxury construction over non-luxury at the same unit scale is usually less than the return. On top of that, at certain scales of operation vacancy is apparently less of a drag on nominal property values involved in the accounting and financing, which means prices tend to float down when the fall rather than plummet. Though of course, any potential developer doing the math is going to look at vacancy rate and will make their decision about whether/what to build targeting points short of outright surplus.

There are some types markets where I think you can drive down pricing market-wide by coming in from the top (consumer tech sure seems to work that way) and that's my guess why so many seem think the same must apply to housing. Perhaps housing could indeed work the same way if the actual manufacturing techniques and costs were being iterated with the same speed and scale.

But that's why there are specific drives for affordable housing: building at the top slows/stops price increases but only lets people on the verge of being priced out tread water.

Personally I think there needs to be vacancy taxes proportional to the market segment being operated (probably also correlated to tightness of supply) so that prices clear on the falling side more easily, but who knows how that would change people's construction calculations.