To doze means to fall asleep or to sleep into a light sleep while assoupir means endormir, i.e. "to make someone/something fall asleep":

Le ronronnement du moteur a assoupi les enfants.

English seems to lack a single verb translating assoupir or endormir so uses periphrasis like "to put someone to sleep".

When the person being "assoupied" is the subject, which is by far the most usual way assoupir is used, the reflexive form is naturally expected :

Les enfants se sont assoupis à cause du/grâce au ronronnement du moteur.

On the other hand, courir doesn’t mean to make someone run so the reflexive form is not needed.

J’ai couru un cent mètres.

There are however a few reflexive usages with courir:

Les enfants se courent après.

Le marathon s’est couru sous la pluie.

and even (colloquial):

Je me suis couru un petit cent mètres.