I'm hesitant to concur with you on the home inspection. The home inspector I've used several times has discovered termites, and other massive problems that would have cost me upwards of $40,000 on one specific house I was interested in buying. I paid a few hundred bucks to save myself from that headache.... The realtor on the other hand did almost zero
In Arizona, every stick-and-stucco house has (or will have) termites. The inspector already knows the answer before he shows up. You pay for "treatment" each time the places changes owners.
When I sold my first house, The buyer's inspector "discovered" termites which would need treatment. However, I had preemptively paid a professional to do treatment just two weeks earlier. When I told the new inspector this, he called the previous inspector. After talking on the phone for 2 minutes, they agreed that I was termite free!
As long as someone got paid for treatment, they were happy. I doubt the buyer knew it went down that way.