Benefit to covering pasta while cooking? Taking a quick poll of several bags of pasta in my kitchen, about half recommend keeping the pot covered while cooking1.
This is not very convenient for me, as I don't have a good tightly fitting lid and the pasta often foams and boils over and cleaning the stove takes longer than cleaning the pot and plates.
So what are the benefits to keeping the lid on while cooking pasta? The main ones I could imagine are less heat loss (but my stove even on min setting maintains a boil, so I can't save any gas) and hotter air above the water (but the pasta is full submerged, so this wouldn't seem to matter).

1 Admittedly, some of the packages were fairly ambiguous as to whether the covering should be done only for the initial heat-to-boil or for the entire cooking process.
I see a benefit to covering the pot while bringing the water to a boil, as you will reduce evaporative cooling and get to temperature quicker.  I might also allow, that in some cases (maybe frozen pasta or too much pasta to water), when you add the pasta (thus cooling the water) replacing the lid will help return it to the boil quicker.  However, boiling pasta with a lid simply invites a boil-over situation.  Once boiling, covering is not influencing the cooking of the pasta.  Just leave it off.