What purpose does it serve to make it hard and expensive for people to file taxes?
Republicans have made it a matter of cultural identify to hate and distrust the government, and the IRS is one of their favorite whipping boys. Keeping it hard and expensive to file taxes is kind of the point - people will like their government less because of it.
otherwise they take a hit on revenues
That's all part of their strategy to "starve the beast", so as to justify cutting social programs or other things they don't like in the name of fiscal responsibility. Nevermind that when they're in power they're just as profligate and irresponsible as they always claim Democrats to be.
spend inordinate amounts of money chasing people who fail to file correctly
Yes, but they like to pick on those people. Those people are not people who failed to file correctly due to our byzantine tax system: they're moochers and freeloaders (and probably commies!) trying to stiff Real Americans (TM). Besides: it's much easier to shake down those people than to go after the more difficult and complicated tax avoidance schemes of high earners, who like to make big campaign contributions as well as stiffing the Treasury.