Database backup fails
The database backup from Craft is slightly different to the SQL export in phpMyAdmin. Craft’s export (presumably) assumes you’re going to want to import that data into an existing site, whereas phpMyAdmin’s default (presumably) assumes you’ll want to import it into an empty database.
However you can do exactly as you suggest — export from phpMyAdmin locally, create a new Craft installation on your live server, use phpMyAdmin on the live server to delete the new database’s contents, then import the original data with phpMyAdmin.
I did this a few months ago (long story); it worked fine, nothing has exploded so far.