Mortgage rates track more closely to 10 year Treasury notes and not by the Fed's discount rate based on my findings of late and tracking mortgages over the past few years.

The Fed funds rate doesn't really do much to near-term mortgage rates (at least it hasn't to me, as a consumer). The market dip in Treasuries (openly traded) depressed yields which drove mortgage rates much lower before the fed acted at all. Lower rates allows buyers to purchase a lot more home than they otherwise would have which has a good chance of being higher than any rise in the market price - especially for less frothy areas.

If you're talking about prices going up as institutional investors buy up property obviously disregard the above as it's a different dynamic.

This reduces the interest on your mortgage

If you already own a home. Otherwise housing is just more expensive. Lower interest rates mean houses can be sold at higher prices for exactly the reason you gave.

It comes down to what people that want to live in a particular area can afford to pay monthly for housing and taxes. As interest rates go down, bidding will increase on homes as people consider the monthly cost which is generally mortgage + interest + taxes.

The only real effect it has on first time buyers is coming up with a percentage based down payment. But 20% isn't a real requirement nowadays, but you will incur a PMI payment until you get to 20% equity.

But housing isn't more expensive, unless you want to pay cash for the home. Then yes, low interest rates aren't nice. But when interest rates are low, what's the point in paying cash? Someone offering you money below what you could make on that money in the open market is something you should take. Put enough down to give you a comfortable monthly payment (or get to 20% to avoid PMI) and diversify the rest of your money.

Sure, price and yield are inversely related, but I would imagine there would be less demand for new housing in a worse economy bringing prices down

The entire point of housing policy at the local level, where it matters, is to make housing more expensive because people's wealth is in their homes and they're relying on housing prices to rise steadily. Renters have less political power.

Local policy is broken but I’m not convinced that it dominates. The Feds have the mortgage interest deduction and Fanny, which both stimulate the demand side very greatly.

Aren't significantly fewer (tens of millions?) people taking the mortgage interest deduction due to tax reform that doubled the standard deduction? Doesn't seem to have driven a collapse in housing costs.

We need more density in low-density areas of cities. Allow people to have multi-family homes if they choose it.

at the risk of getting into a political debate on the internet: I hadn't heard this. Do you have any sources backing up this claim?

that....doesn't necessarily correlate with making housing more expensive, though. There are government-funded housing programs in other countries that they may be referencing as a model, for example.

If it “builds wealth” faster than any other means then it necessarily becomes more expensive for new entrants. This is an inescapable outcome.