It's a bargaining chip to get votes. If one party promises a larger tax saving on homes, then homeowners are more likely to vote for them.

Besides that, there may be some societal benefits to increased home ownership.

As I understand it, mortgage interest deductibility was originally basically social policy (rightly or wrongly). And you can't take a benefit like that away--even if the government kind of did for most people by increasing the standard deduction. (Which was probably not a terrible way of doing so.)