Some people are very careful not to put anything with seeds on the compost heap. Personally I don't bother. It's easy enough to hoe off anything that appears in the garden and sometimes you get bonus worthwhile plants.

I feel hoeing works less well in wet weather ,but yes I also get bonus plants such as spinach ,parsley and broccoli.

Lamb's lettuce also seems to self seed like topsy but is not the most popular ,unfortunately.

Yes, hoeing isn’t great in damp soil. In that case I just weed by hand. I hate the idea of sending anything green to landfill or burning it so compost is my default.

Are you in the UK?

No ,but this is the Atlantic seaboard and we get a lot of wind and rain.I am starting to use seaweed but I am learning that you need to have some more constant form of humus as well and I don't want to add seeds to beds that are starting to encourage me that I might be able to get on top oft the huge amount of weeds I have had this year,

I don't put weeds in my compost, so just have fruit and vegetable seeds. I've been getting one volunteer pumpkin vine each year for the past few years and many volunteer tomato plants, which I pull out or give away.

In weedy areas that I don't want to deal with, I spread newspaper topped with seaweed and covered with something pretty like compost or leaves.