Rereading Edmund Morgan, American Slavery, American Freedom: The Ordeal of Colonial Virginia (New York: W. W. Norton, 1975) for my current project, The Poverty of Slavery, I was reminded of Thomas Jefferson's disdain for debt (aside from his personal addiction to it). His argument was that debt created dependence and that dependence made republican government impossible because it allowed one man to control another man's politics/vote. (Ironic, yes. See Morgan for details.)
From this, I believe, came the dumbed down notion that homeowners have more of a stake in the community (and perhaps even society) than leaseholders do and hence the notion that government ought to encourage home "ownership." That homeowners have a greater stake is certainly true when people actually own their homes, as oppose to "renting them from the bank," especially when leaseholds are short (as they are today).
But the mortgage interest deduction, one of the causes of the '08 crisis, does not encourage real ownership, it encourages "renting from the bank," i.e. staying heavily leveraged (high loan to value). If the government was really interested in promoting stakes in society, it should change the mortgage interest deduction to a mortgage principal deduction. The tax benefit would be light in the first years of a 30 year amortized mortgage but get progressively heavier over time. That would discourage using the house as a piggy bank (refinancing to cash out equity) and encourage 15 and 20 year mortgages, which dig into principal more quickly, and eventually outright owning homes (no mortgage), which is what Jefferson wanted after all, if a tax deduction were also allowed for outright ownership, up to some reasonable limit of course.
I would prefer a flat tax in the sense of no deductions whatsoever (at lower marginal rates of course) but if we have to have a deduction or two (for political reasons) then a mortgage principal deduction would be more in line with republican theory than the interest deduction, which encourages the wrong behavior (from the standpoint of everyone except mortgage lenders).