The primary (sadly, pun intended) advantage of running a normal full backup is that you can leverage differential backups to cut down on backup time and resources used when you run differentials instead of fulls.

Running a copy-only on the secondary has the wonderful advantage of not taxing resources on your primary production server, but doesn't reset the differential base (and differentials aren't allowed against secondaries anyway).

Copy-only fulls against the secondary are great for backups that aren't used for data protection (refreshing data in a dev/test/sandbox server, for example), since you can take them without hitting your primary server.

For protecting your data, though, it's probably best to run regular full backups on the primary, just so you can actually use differential backups.

Just my $0.02.

Cheers!