Thanks for all the replies!
We didn't get much of a carrot crop due to weeds outcompeting them. So I will treat the carrot/parsnip beds next year to an extra deep mulch of imported compost (easy to have a delivery as there are tons delivered for the fields) and try the false seedbed technique, i.e. hoe once or better twice, letting weed seeds sprout in between. Same treatment for my seedbed.
I plan to do a lot more transplanting next year, multisowing in modules, which get planted with larger distances, so I can plant and mulch first, weed second, so I can feed the soil and minimise weeding at he same time.
My garden partner is paranoid about weeds, even in our wildlife strip... and dock on the field next to the garden gets herbicide. So for that particular plant, probably pull. The rest, pull and drop if they get too big, give to the chickens if they've set seed.
The zone aspect is an important one, chop and drop does require not missing any seed setting weeds! It is also a question of the size of garden you have...