I don't think your method is necessarily unfair. I just don't think it necessarily is fair, either. If all of your roommates have roughly equal views on the value of money, square footage, and various intangibles (such as, say, the quality of light in a room), then your method is probably entirely fair -- no arguments there. If, on the other hand, they each assign very different values to space or money or those various intangibles, then it's possible that -- despite paying similar amounts of money for similar amounts of space -- they are actually experiencing very unequal levels of economic utility in exchange for their rent. Which would be where something like the NYT algorithm begins to make sense, since this attempts to maximise the utility function for all parties, regardless of how they themselves define utility.

As for the cleaner: yours is a very common reaction that I get whenever I give this advice to my friends. But professional cleaners are surprisingly affordable. In multi-person households -- unless you're living close to the poverty line -- they should be entirely affordable (much less than the proverbial cup of coffee per day), and go SUCH a long ways towards reducing household drama! Have you tried actually crunching the per-person numbers? You might be surprised at the results.