I'll often do Tojil with 7-8 people, with a rdm and maybe a geo in the second party.
It's far easier for a rdm to manage haste cycles than a whm. 3 minutes is annoyingly short, whereas Rdm can get 6 minute hastes with Composure. If there's a sch for stunning, losing Marches isn't nearly as bad if you still have Haste II on. Plus that means the brd doesn't have to special case the sch songs, and can just ballad+ballad+march for both the sch and the whm.
With Distract II, there should never be any issue of needing Madrigal, even with weaker DD gear sets.
With both of the above, the brd thus doesn't need either a second March or a Madrigal, which means all remaining songs after the first March can go to Minuets. That should be worth at least another 70 attack (about +5% damage).
If there's no cor (as there often isn't in 6-man groups), Dia III provides an extra 5% def down (about +6% damage, or +7% with a geo doing def down).
The rdm can heavily enfeeble NMs (para/slow/silence), making everyone's lives easier. Fewer attacks means both less for the whm to heal, and less time stunned (in the case of Tojil) for the DDs, which improves their damage.
And if they're bored with nothing else to do, they can add extra damage with nukes.
Basically, a perfect group certainly doesn't need it, but it vastly improves the safety net of an imperfect group (as pick-ups tend to be), and even for a perfect group, it just makes the run less of a hassle. Since I'm the one that often has to deal with the 'hassle' side of things, I'm always happy to take one along.