I think that there might be a slight misunderstanding : you are talking about swordmanship in general, while I am talking about sport fencing with the épée, or at the very least swordfighting with thrust-centric weapons such as the rapier.
I am not qualified to comment on circular movements in general and I am aware that many systems, namely longswords, sword and buckler, British military sabre and japanese kendo use circular movements at least to some extent.
However, I strongly disagree with you in the context of fencing (épée) or say, duelling with a smallsword (from which fencing is derived). How are circular movements supposed to be more efficient when using thrusting weapons which are "linear" in nature? It just doesn't work like that. Straight movements will always beat circular movements in this context.
Also, contrary to boxing, which you like to mention, there is no room for error, because it takes 750g of pression to get the point in épée and and even less to puncture the lung or juggular of someone using a smallsword. So you can't evade lateraly a thrust. It's not like just slipping a jab because there is no room for error.
I also disagree that linear means brawling or that a lunge is inherently a telegraphed attack. The lunge is the most efficient way to cover the most distance in the smallest amount of time. There is a reason why it is used and trained so extensively and a properly executed (with the right timing) from a good fencer hits you before you even had time to react.
Lastly, I think that modern fencing would look pretty much the same even if circular movements were allowed. You can move to the side left and right all you want, but you still need to attack in front of you in the end.
Just my opinion, though.