Am I looking at a screen porch with some repurosed shelves that were once indoor? They do not look like typical redwood or even treated exterior pot shelving? They are not laminated particle board or something are they?
Anyhow, I guess you could use expoxy liquid wood fillers followed by expoxy paste to repair the shelves. I used Abatron products but ConservEpoxy products are great too. The expoxy will cure harder than the wood ever was but the stuff is not cheap and whether it is worth it depends on how badly the shelves are rotted. I cannot really tell from the photo. If they are made of material that was never intended to be outside, I think I would just get rid of them and start over.
Basic shelving is among the easiest things to build (or have built) so I think you will find it easier to start over with some nice redwood or treated material. Do build with better attention to drainage. You probably do not want a bottom shelf so close to the ground with real garden shelving (again I suspect your current shelves were repurposed from an interior use?).
Bugs should not be attracted to shelving any more than anything else but of course they like hiding in dark corners and some where organic matter like potting soil builds up. Spiders feed on other bugs. With shelves better suited to being in an outside environment and with drainage built in you should be able to hose them off to keep bugs from nesting.
Whether you just get rid of them and do not rebuild is up to you. You live in a climate where I think have shelves for potted plants is nice. I lived in San Jose and was able to grow many varieties of orchids outside. In San Francisco, 45 minutes away but on the Pacific for all intents and purposes, and even more directly influenced by the ocean and fog, you can even grow more and have a wonderful hybrid orchid nursery near you. You can also grow lots of what most of us consider houseplants on protected patios. Having a place to put different sized potted plants is nice I think? So long as you watch for insects bringing them indoors, houseplants really benefit from an outdoor vacation.