Was just thinking about this one. Dual-wielding has the inherent penalty of preventing shield-use. So there should be some benefit, right? I made a short list earlier, but it seems that wielding two weapons should give the wielder more options for ending/injuring opponents. That translates to more damage or more attacks or more maneuvers. But...balance. Dual-wielding can't become the ONLY choice (even if it's a good or bad one).
The use of a heater, kite, large lozenge, or large round shield really don't take much thinking; they do require a lot of training to get to consistent utility. An off-hand weapon, however, imposes much more cognitive load to be able to use it for extra attack options; using it purely defensively is still more than a large shield, but on par with a buckler/small or medium round/targe/small or medium lozenge... because those all require active defense .
It's a vey complex interaction of weapon choice, training, available cognitive ability, the same for the opponent, and the situation.
If I were to face Master Nytshaed again, I'd really rather use buckler and single sword with him using case of rapier (dual), because case is is slowest form in SCA rapier last we met. And I'm most comfortable with buckler and single. Of course, I expect I'd lose 5 for 6 vs him... even stacking the odds that way.
Likewise, in rapier, lacking an off hand is NOT a real penalty; if one's well trained in singlesword, their defense and riposte make a one-on-one very much a matter of being faster... or managing to compromise their sword. THere is an advantage to whomever has the longer reach, but even that's not telling... my reach is about 6" more than Nytshaed's, but his mastery of footwork more than makes up for my reach, and even when I'm using a further 4" more blade...
Then again, my pessimism about beating him is entirely because he was one of three individuals I studied rapier from.