... has anyone here ever tried simply letting basil go to seed?

I allow basil to flower and go to seed because the blossoms attract hordes
of pollinators and I want to encourage them. I've had very few volunteer
basil plants the following year. Presumably the seeds are not frost-hardy.

I allow dill to flower and go to seed for the same reason. My garden hosts
a lush growth of volunteer dill every year. It's easy to understand why
some people call it dill weed.

Daniel B. Martin