I really don't think that absentee ballots can be abolished. I agree that a lot of people who vote absentee that I know are entirely capable of early voting and voting on election day, and really have no pressing reason other than convenience, to vote absentee. All are citizens and I see no reason why they should not be allowed to vote absentee.
Most of the voter fraud we have here is caused by people who deliver absentee ballots to old folk's home and other institutions, then deliver them to the polls. In cases where the voters themselves request, fill out and mail in their ballots, fraud is minimal to nonexistent.