I've worked for one of Europe's biggest synthetic biology labs and I know lots of biologists are low-key interested, but current players in semiconductors see it as kind of a tarpit.

IBM used to have a program using DNA origami for lithography back in 2009, which makes sense as lithography masks are a pain to make. I really wish I know why the program was stopped, but most of the researchers are retired by now.

As to whether you can just "grow" the whole chip from scratch, the answer is probably, but it would require lots of non-trivial scientific discoveries. For instance, we can't really make sizable chips using DNA without horrible defect rates. Biology is much better at making redundant rube goldberg machines, than very precise machines with no tolerance for errors.

I think we'd have a better chance of success if we made very weird kinds of chips that better took advantage of the medium, perhaps even something that we "train" rather than just use out of the box.

I'd love it if anyone here knew more about this !