FAQ - Answer
First, Blue Oaks tend to be good sprouters. The sprouts can provide suitable browse for deer and also perches for rodents, like ground squirrels. If maintaining attractive wildlife forage and other habitat elements is desirable this may be a consideration. Leaving the stump will prove to be an obstacle if range seeding is desired in the future. The stump will eventually decompose into the soil. However, the loss of annual leaf fall has shown to affect soil productivity over time. The loss of annual leaf fall will affect grass productivity more that retaining the stump. Simply cutting down the tree and leaving in place is the least expensive. Removing the tree adds the cost of time and energy to transport the tree off site. Finally, removing the stump is another cost factor since heavy equipment will be needed to remove the stump, fill the hole and remove the stump from the site. All of the discussion points have merit.
You might also take a look at a recent article in Cal Ag on oak thinning in Shasta and Tehama Counties (Standiford, R.B. D.D. McCreary, S. Barry, L.C. Forero. 2010. Blue Oak Stump Sprouting on California’s Northern Sacramento Valley Hardwood Rangeland. California Agriculture 65(3):148-154.) The Guidelines for Managing California's Hardwood Rangelands also has some good information about thinning recommendations for landowners (see ordering instructions at: http://anrcatalog.ucdavis.edu/GrasslandsHardwoodRangelands/3368.aspx)