We didn't want to have to battle for access to the ISP's premises at 11pm Saturday night to be able to reschedule a backup or indexing run. A number of issues come under the umbrella of database administration. Security entails defining users, granting them access, and checking to see that they don't violate their given rights. In addition, you need recovery provisions to restore the database in the event of a serious failure. Pray you never have to do this.
Performance also counts, naturally.
And again, with the division's production server sitting on an ISP farm, we didn't want to have to regularly run in there, or sign on, to do performance optimization runs. If we were only considering remote operation we would have picked a desktop version of one of the DBMSs. They're a snap to manage. They can run for ages with stable performance and minimal DBA intervention. They don't require regular performance tuning runs.