Such a chart is not a paradigm of forms of the “same” word, but rather just an array of related but “different” words. What justifies this statement?
It’s often not even clear what should count as filling the slot. There may be several possible candidates for a particular slot, with various meanings. Should the adjective for cat be catty or feline? One is closer in form (i.e. it shares the same root), but the other is closer in meaning (it refers to cats rather than the behavior of humans). There’s also not a consistent relationship between the related forms. The relation of talk :: talked is exactly that of run :: ran, i.e. past tense, because it is inflectional morphology that is involved. But despite the meaning of to water, the verb to knight doesn’t mean “to sprinkle with knights”, but rather something like “to make into a knight”. This type of inconsistency is the norm for derivational morphology. The way the slots are filled is often quite erratic as well. Notice some of the many ways verbs can be changed into nouns in English.