To determine whether auxiliaries are verbs, we should examine two kinds of properties. One kind of important property relates to word forms, and the other kind of property relates to word use.
Most verbs have properties such as tense, aspect and mode.
The verb to be is a normal, complete verb. Was and were are past tense forms of to be, and is, are and am are present tense forms. Being is a continuous aspect form, and been is a perfect aspect form. The were of "if I were a rich man" and the be of "be he live or be he dead, I'll grind his bones into my bread" are subjunctive forms.
If can is a verb, then it is a defective verb. It doesn't have forms that show aspect. The forms canning and canned don't exist for the auxiliary. Neither does the infinitive to can.* However, it does have the properties of tense and mode. Could is both a past tense form and a subjunctive mode form, just as were is both a past tense form and a subjunctive form of to be.
Word form isn't the only way to show a verb's mode. The interrogative mode is usually shown by the verb's position.
The statement "he is a student" employs the indicative mode. The interrogative mode places the first word of the verb** before the subject: "is he a student?" The statement "he can be a student" is subject to the same transformation: "can he be a student?"
A clause pairs a subject with a predicate. A predicate requires a verb. We consider a statement like "he studies" to be a complete clause. In answer to the question "is he a student?", the answer "he is" also counts as a complete clause. If, in answer to "can he be a student?", the statement "he can" is a complete clause, then the can must be a verb.
Although we can see that the auxiliary can doesn't exhibit every property that most verbs have, it does exhibit properties that only verbs have. It has a form that marks tense or mode. Its position can indicate a mode that word forms cannot. It can act on its own as the predicate of a clause.
All these reasons support the idea that defective verbs are verbs. We don't have a good reason to place such words in a different grammatical category.
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* Yes, there are homonyms that do have continuous, perfect and infinitive forms. We won't consider those to be the same verb.
** Most one-word verbs require that a word be added to the verb phrase so that the added word can be moved. The statement "he studies" becomes "he does study" on its way to becoming "does he study?" The notable exception to this is when the one-word verb is a form of to be.
Best Answer
Because we already have replenish for that purpose.