The weeds discussed in this article,
Amaranthus tuberculatus and
Amaranthus palmeri, are exactly the kind of plants that early human cultivators would have selected as a seed crop - fast-growing robust plants that could be continually selected for maximal seed size and minimal toxin production generation after generation (which is how crops like maize were developed). Indeed members of this genus were used by Aztecs and others for just that purpose:
https://en.wikipedia.org/wiki/Amaranth_grain
As far as maintaining fields, area spraying of pesticides and herbicides will be replaced with robots wielding lasers and using AI image recognition to catch pest infestations before they take over entire fields.