Part of the reason could be that organic materials will burn off above that temperature and skew the results.

When you are contemplating Atterberg limits, you are generally talking about clayey materials, and particularly plastic materials.  The reason for the limits on the temperature is that higher temperatures will actually drive out the moisture within the clay particles, thus inducing very high van der Wals forces or the forces that make clay particles bind together (that's why we can "fire" clay and get pottery).

I would generally NOT use oven drying for clayey materials...they will dry adequately with a bit of manual manipulation in a "laboratory" humidity environment.  If you must use something to dry the material toward its plastic limit, use a dessicator.

In my laboratories in the past we have limited the temperature to much lower values (105F or so).  So what if it takes a bit longer to dry....hopefully that's not the only thing you have to do!

Ron gave a good reason for not drying at high temperatures when 'adjusting' the water content - there is 'held' water within the clayey structure that is not free and you don't want to drive it off - see Zeevaert's book, I believe, on this subject (Mexico City clays).  I believe that the old US Army lab testing manual required oven dried material to start off the test -  Lambe (1951) didn't.  We, in our labs, always used the natural moisture content and then adjusted up or down by letting it dry naturally in the lab.

In order to have the material preped to pass the #40 sieve using the dry prep method (not as accurate as the wet prep method) the material must be dried enough to be pulverized in a mortar using a rubber covered pestle.

If the sample is suspected to be organic, one portion should be "oven" dried and the other portion of the sample either wet preped or dried at a much lower temerature and dried preped.  if there is significant organic content there will be a significant difference in the liquid limits of the 2 portions.

I understand that to dry a sample of clay or clayey soil at a high temerature, the "water of chrystalization" may be driven off and therefore, chemically change the soil.