FHE has a lot of properties beyond just those needed to search a db. If you have a specific application in mind there may be more efficient things. E.g. if you want to keep secret what you are looking at but server knows the keys, see research on private information retrieval. See also some of the research on order preserving encryption and the like (although lots of those schemes have questionable security properties). Of course everything has tradeoffs, but often "perfect" security is unnessary in an application.