Sorry to hear it. This brings back lots of memories, and not the good kind. What follows is just a personal view point, but it has worked for me.
Getting rid of dampness, e.g. traces of water, really helps. Humidity helps them thrive. This is not, repeat not, a criticism of your wife's cleaning habits. Once springtails get in, dampness enables them to thrive. Unlike roaches and silverfish that do pretty well in drier areas, springtails really need damp/water, and they feed on any trace of food residue or mold that grows on food residue.
Does your refrigerator sweat? If so, add cleaning it regularly to the list, as household dust plus the sweat will harbor springtails.
I wonder if the compulsive cleaning leaves counters and crevices wet/damp enough to enable the springtails to thrive and feed on the residual organic matter, and general fungal growth. So drying surfaces with clean towels after cleaning is going to help. (Wash the towels after use on a sanitary setting with bleach. Just do not leave damp towels to dry in the kitchen area. Costco stocks bulk towels to help with the use, and then into the wash cycle.) Microwave sponges after use, and keep them elsewhere.
If you have stone or tile counters/backsplashes, I would recommend removing the existing caulk and then recaulking and resealing the stone and grout, and seal any penetrations. I'd add outlet foam seals if they aren't sealed already. It is a pain, I know, but the springtails will exploit any bit of residual organic material and water. Don't overlook sealing the seams at the toe board /kickboard to floor, and to the cabinets. If the floor is not seamless, e.g. wood, tile, or not seamless linoleum, that should also be resealed.
Don't forget to stopper drains, and overflows if possible. Yes, this is a war.
While I think bleach is your friend on compatible surfaces, I wonder if switching to orange oil cleaners and using boric acid around the edges might help. The active ingredient in citrus cleaners, d-Limonene, is very hard on insects. (
Summary @ EPA )
I have springtails mentally filed with roaches and silverfish as feeders of residual gunk, but collectively hard to get rid of without getting compulsive about keeping counters and sinks free of anything organic, especially if there any cracks, however small. So, no food on the counter, no coffee or coffeemaker, no sugar bowl, no cookie jars, no fruit, no onions/garlic, no bread bins, nothing. Use dishwasher compatible cutting boards and clean them. Keeping food (flour, sugar, crackers, nuts, cereal, everything, all the time.) stored into sealed containers helps (e.g. glass jars, plastic with seals, etc.).
Once things are under control, then I think that the coffee maker can go back to living on a counter, although cleaning any spilled grounds is going to need to happen after the coffee is consumed every day. Personally I would not relent on anything else. I have the view that something in the local environment probably predisposes your kitchen to being great habitat, and there is no need to tempt springtails back into running wild.
If it were me, I would check the AC drains and filters as well, especially if you have mini-splits. Just because you find them in the kitchen doesn't mean that they are in the kitchen for their whole life cycle.
All the best,
Peter