From the Joint Committee on Taxation's General Explanation Of The Tax Reform Act of 1986, page 220:
Congress concluded that rules that encourage filing separate returns give rise to unnecessary complexity and place an unwarranted burden on the administration of the tax system.
Although this section of the document is not about IRAs, this act altered the IRA contribution rules among other things, and that statement appears to be the general philosophy: the government just doesn't like married couples filing separately, and essentially tries to punish them for doing so. Note that the same income limit applies for deductible contributions to Traditional IRAs, if either spouse is covered by an employer-provided plan (see here).
This page suggests one such incentive for the IRA in particular: "The rationale: the government doesn't want to give you a tax break in case your spouse is high-income". If one spouse is earning a lot -- for instance, over the Roth IRA limit -- and the spouses are living together, the other spouse is presumably reaping some of the benefits of those high earnings, so should not be allowed to benefit from the Roth, which is supposed to be unavailable to high earners. Also, if one spouse had earnings over the Roth IRA limit, they could possibly use financial sleight-of-hand to shift some of the income to the other spouse, thus enabling both to contribute.
I don't see that these reasons really justify the drastic nature of the penalty, but I think that's about as much logic as we can hope for in the tax code.