I ran screened bottoms last summer.
I saw beetles going up through the wire.
I saw beetles get chased out through the wire only to do a U-turn and go straight back in.
People say beetles can't get in through screened bottom boards and I believed it too until I watched it happen. The only good thing was the screen gave the bees somewhere to eject all the SHB larvae that almost destroyed their brood nest (coincidentally I had a tray of water under the hive due to a heatwave so most of them drowned).
I have recently started using these:
https://hiverly.com/guide/There's no SHB around to test it out but based on other peoples experience they work very well.