I didn't pay an absurd amount of money for my house because the market was super hot and I had to outbid everyone in a bidding war (though I did have to do that).
I paid an absurd amount because with interest rates so low, it was cheaper than renting in term of monthly payment + maintenance.
I'd obviously be willing to go as high as my current rent, and probably a bit higher (to be allowed to do whatever I want with it), and that just came up to the price I paid.
The only thing blocking you, financially, is the down payment. The lower the interest rate, the higher the down payment will be for the same monthly payment. That's the problem.
To live in the house, if you can afford 1500/month (including insurance, HoA, maintenance), it doesn't matter if the house is worth 100k, 300k, 600k, 1 million...if the math adds up to 1500/month, you'll buy it. Interest rates go down, house value go up. Simple as that.
Now if you add all the other factors, like how home ownership becomes a potentially profitable investment, alongside society's pressure that "it's what you're supposed to do", and of course prices will skyrocket, shortage or not.
In turn, it raises rent prices, which makes the math above work out even more, and it's a self reinforcing cycle.