The same principle applies to working with knives. We drill and fight with training knives the size of folding knives, through to tanto, dagger, Ka-Bar size, and even Bowie knife size. By doing this, we learn to defend against all kinds of knives, and can quickly adjust to defending or using a very small knife or a large heavy knife.
There is a massive difference between defending against or weilding a folding knife and a large utility knife. The speed and weight difference of such knives is significant, and unless you are familiar with these differences, standard drills done with only one specific training knife, can be difficult and even put you in dangerous situations.
Weapons training and especially knifework classes really improves footwork and co-ordination. A regular weapon training class starts with a warm up, then advances to basic movements and strikes, then over to dissarming techniques.