You have two hands to punch and grab, and two legs to kick with. Kicking is common in many martial arts from the Eastern Hemisphere, but most are unaware of the foot-centric Western Martial Art that is still practiced today called savate.
Modern boxing is to pugilism as today's savate is to Victorian savate. The techniques you see in the modern versions of these sports are a reflection of the rules and conventions of the sport, and not necessarily the most effective for defence in a surprise attack situation.
Savate literally translates to "old shoe" and is intended to be practiced in shoes. The modern sport features special boots, and most savateurs practice in soft tennis shoes. It is certainly more practical to learn to kick in the footwear you'll likely be wearing in the case of a mugging, both for the foot that hits and the leg that supports you on the floor, rather than in bare feet as in most Eastern martial arts.
Barton-Wright also made this cryptic remark: "[Savate] is quite useless as a means of self-defence when done in the way Frenchmen employ it." Some speculate that this refers to the kicks used in Cornish and Devonshire where the weight is kept evenly on both feet, as in pugilism, compared to the French who transferred their balance entirely over one leg for higher and faster kicks. It may simply refer to the hand positions, in which savateurs often throw their hands away from their opponent to execute better kicks.
The stance for savate is exactly the same as the stance for bare-knuckle boxing, and all advice given to English boxers was echoed in French.
It is especially important for the lead foot to point toward the opponent to facilitate savate's fastest and most effective kick: the shin kick.
Savate has a unique kick called the coup de pied bas or the shin kick. It used to be featured in other martial arts, but it was banned from most forms of competition because it was too effective at breaking the knee joint.
The shin kick targets the knee or shin, striking with the heel in a kind of forward stomp. It can lead to tendon pulls, shattered bone, or a sprained ankle depending on the angle of the strike. In many ways, it can end a fight quickly.
Low kicks like the shin kick are fast and surprising because they do not enter the peripheral vision. The savateur also does not telegraph the kick because it does not require a hip turn or change in hand position for balance.