“I wonder if there is any constitutional reason it can’t be used to pardon illegal aliens.”
Generally one has to have been arrested, tried, & convicted before they can be pardoned.
Nixon?
Nixon?
Actually, there are many examples of individuals and even entire groups being granted pardons, throughout American history. Washington pardoned insurrectionists.
http://www.usconstitution.net/consttop_pard.html
Andrew Johnson pardoned, with some exceptions, the entire South, and then later pardoned most of the exceptions.
http://www.sewanee.edu/faculty/Willis/Civil_War/documents/AndrewJ.html