Matt's specific reasons that "sport fencing" has no reality to it:
No. 1 - It is done on a narrow piste
This is, imo, one of the easiest to dismiss.
"sports fencing" is based on specific weapons - currently at the Olympics these consist of the "foil" (i.e the fleuret), the épée [de combat], and the [Italian light] sabre.
Originally, the only Olympic weapons were the fleuret and the sabre. The épée was added soon afterwards. Singlestick was an Olympic weapon briefly (iirc as a demonstration event - I'll confirm one way or the other if anyone wants). Rapier and dagger was also proposed as an Olympic event, but never formed part of the Olympics.
The epée de combat is a late-model small-sword blade, set with a cheap steel guard. The fleuret has remained unchanged bar the coquille for even longer than the epée's blade. The (Italian Light) sabre is the foiled version of the Italian duelling sabre, which is itself a derivation of a late-model spadroon.
The key thing about all of these is that they are all late-vintage, lightweight weapons, and so are considerably faster to wield than their fore-runners.
Let's consider, for example, the épéé. It's a late model smallsword, with a different hilt. The small-sword, over its evolution, became gradually lighter and shorter. Even the early smallswords are lighter and shorter the preceding rapiers.
The rapier's typical blade length is 39", as opposed to the small-sword's 33" or less (although there are smallswords known up to 35"). The comparison of blade-weight is made clear in the colichemarde transitional blades - fortés as large and heavy as a rapier's, with a mid-section and foible as small and light as later smallswords'.
So the smallsword (and consequently the épéé) is much lighter, and has a much lower moment of inertia than the rapier. This makes it much faster to wield than the rapier. And so styles of fence change markedly over the transitional period.
One key difference is that periods of fencing time for blade actions become much shorter.
The human body doesn't alter much however, so periods of fencing time for body movements do not shrink.
Previously, you could circle your opponent for advantage in line. With the smallsword, the defender can cover an arc of about 120degrees at a radius of about 50" to 60", without the need to move his feet at all.
An attacker wishing to evade this defensive sweep needs, therefore, to cover 52" to 62" to bypass this defensive sweep - four-a-half to five feet, or more. About four or five periods of fencing time, as compared to the one period of fencing time the defender requires to counter it.
Unsurprisingly, circular movements to gain advantage wither as a consequence, and displacements become increasing small, and increasingly linear. The volte and demi-volte are still emphasised during the period of the transitional blade forms, but become gradually less emphasised, leaving the inquartata as the only important sideways motion by the time that the smallsword is itself transitioning into épée de combat.
(Incidentally, the inquartata popped up in a thread recently - possibly even this one. Someone asked if it was even used or taught anymore. I can confirm it gets used - used discriminately and with excellent timing, it's highly effective. And I can confirm, as my own Master still teaches it, as do I, that it is still taught).
So, it is the reality of fencing that changes into a linear form, which in turn then gets reflected into the terrain de combat.
It is not an artificial restriction, it's a difference that makes no difference - for the reality of that specific weapon.
As a quick check - I went to the Smallsword Symposium's videos and watched the free-play, where there are no rules restricting anyone to a linear path. You still see linear fighting, rather than fighting in the round.
The only instance that I've seen that veers more than a metre off the centre line results in the attacker, who causes the veer, getting stabbed.
The other veers are smaller and happen when a defender is getting pressed close to a wall, and attempts to then change the path to go along the wall rather than continue stepping back into it. Predictably, in those situations, the defender is hit.
However, smallsword and epée duelling were outdoor pursuits - as Olympic epée also was, originally.