Targeting an all in home payment (principle, interest, insurance, taxes) of 1/3 your $100K income, so $30K or $2,500 per month.
In a world with MID, the ~$1500 in interest payment each month can be paid with pre-tax money. Assume you're in the 30% bracket, that means an extra $450 each month. Now you can afford a mortgage that costs effectively $3000 per month, which comes out to another $50K to $75K in purchase price (rough estimate assuming 4% interest rate).
sounds like a great way to push up prices!
To the extent it factors into the monthly payment people can make, it impacts all the things you list.
The MID indirectly affects the monthly payment on a home. It reduces the effective monthly payment.
Anecdotally, for me; it 1/7 discount on my mortgage cost. (Which I can realize more quickly by adjusting my w4)
I've bought three houses in my lifetime and the MIB was never even in the conversation in any of those purchases.