Ask Mr. Smarty Plants

According to all the arborists I have consulted you do indeed need to maintain these bulkheads to assure your trees' good health.  Tree trunks and roots need a good supply of oxygen, and this is threatened by a thick cover of soil over the tree's base.  It is true that different tree species differ in their ability to withstand stress. Ulmus crassifolia (Cedar elm) is generally very stress tolerant, and Prosopis glandulosa (Honey mesquite) will also survive many stresses (but not chronically wet soil).  However, without sufficient soil oxygen growth is likely to gradually decrease, perhaps over several years, and it is likely that the trees will finally die. 

You might consider constructing or purchasing a metal or wooden platform surrounding the tree trunks at the current ground level to disguise the cavity below. In the case of your mesquite, some diversion of runoff or drainage from the cavity should be put in place to prevent lengthy soil saturation after rains.

Some creek bottom tree species, such as Taxodium distichum (Bald cypress) and Juglans microcarpa (Little walnut), have evolved to survive being buried beneath several feet of gravel deposited by storm water.  If you are a gambler and determined to level the yard you can try to copy that scenario.  Place two or three open two-inch pipes vertically in each containment and then fill the containment with coarse gravel.  This will maintain a somewhat aerobic environment at the base of the tree.  Prevent fine soil from being washed into the gravel by runoff.  There is certainly no guarantee that this will satisfy the tree's needs for oxygen.  One way to monitor the health of your trees is to compare the length of new twigs added each growing season with that of twigs on comparable trees not buried.  If twig growth is sharply decreased steps must be taken to achieve better aeration.

Good luck in solving your problem!