Neither I nor my lovely wife seem to have problems with Desktop icons moving after a Restart. You might want to check your Finder prefs under the View menu. "Sanp to Grid" would be automatically moving them to a 'safe' position at the beginning of their existence, of course. but it doesn't sound like you have that selected. How about "Keep arranged by..."? Generally, de-selecting all the options in that dialog will always leave icons where ever you place them. Maybe not as neat as Apple wants, but it's
your computer, after all.
As a matter of fact, I have two icons moved to the right of their 'normal' position so I can usually see them even with a window near the right-hand edge of the screen. And I may 'suggest' that my wife try using one of the forced alignment options just so she can find (visually) some of her dozens of icons.
BTW, keeping icons on the Desktop
can cause System/Finder slowdowns. That virtual Desktop is actually a large image that must be redrawn each time it becomes visible or parts of it are seen/blocked. Not only that, but the links to the items shown may need to be reloaded into the Systems brain so it can deal with any access attempts by the user. Simply putting the icons into a folder can speed up the process by making things naturally usable in Finder terms.
