While I do pull all the ragweed I see... Prior to bloom time.... You should respect that it generously waits until the end of the season before bothering us with its sexual activity.... And at my house, the deer browse it...
Plenty of other plants are also wind pollinated, the oaks and pecans and stuff in the spring... all the grasses.... All summer long...
Us gardeners in the deep south have some weeds that are actually worthy of the name.
Consider phyllanthus niruri (chamberbitter) and fatoua villosa (hairy crab weed, mulberry weed) which go from seed to flowering plant in 2 weeks...
Also consider nut sedge... One tuber can quickly cover a field in nutsedge....
And while some of that oxalis can be aggressive, due to the tuber production (pulling it merely spreads it), at least it's pretty, and edible... In fact... There's a variety known as oca... Specifically grown for tuber production.... Said to be as productive as stachys floridana... Also an aggressive spreader... But... Those tubers are tasty...
Some of us actually recognize the desirability of stealth gardens containing veggies that grow well in case of TEOTWAWKI...
While we're naming plants with weed in the name that are actually keepers...
Consider coffeeweed and camphor weed.
And... How about button weed? Host plant to the tersa moth.