I only used the terminology 'average middle class' because the parent had. I'm British and terms like working class and middle class seem to have slightly different meanings in the US so usually I try to avoid using them.
Also, even if it is not much of a win for the wealthy households, higher property prices generally mean higher rents so it disadvantages the class of people that rent. A similar argument applies to housing benefit in the uk, which is something you receive if you are poor (working or not). The recipient doesn't really see the money, but it helps to keep rents high so it's more of a 'landlords benefit', much like your mortgage deduction seems to be of more benefit to the banks than home owners.
Just to be clear, there are two problems with the mortgage interest deduction. First, it's regressive; by the numbers, the people who benefit most from the deduction are those least in need of a benefit from the government. Second, regardless of your income level, the mortgage interest deduction artificially increases the desirability of residential real estate, which drives up the prices, which acts as a shadow tax on home ownership.
The first problem you could address by capping the benefit somehow. The latter you cannot.
My microecon is a little rusty but isn't the second problem essentially a wash? It seems that the shadow tax should never exceed the mortgage interest deduction (assuming rational markets).
To a first approximation, the MID pushes up the costs of housing by as much as the tax deduction. Making it entirely useless for "encouraging home ownership."
Also, even if it is not much of a win for the wealthy households, higher property prices generally mean higher rents so it disadvantages the class of people that rent. A similar argument applies to housing benefit in the uk, which is something you receive if you are poor (working or not). The recipient doesn't really see the money, but it helps to keep rents high so it's more of a 'landlords benefit', much like your mortgage deduction seems to be of more benefit to the banks than home owners.