The development of primary and secondary immune responses to an

The development of primary and secondary immune responses to an antigen differ significantly. The primary response may take a week or more to develop fully and establish memory. The secondary response is rapid and relies on the activation of clones of memory cells. Would it not be better if clones of reactive cells were maintained regardless of prior exposure?
In this way, the body could always respond rapidly to any antigen exposure. Would there be any disadvantages to this approach?
Why?