Childhood fears are common, normal — Some behavior, such as nail biting, bed-wetting and fearfulness, may actually represent a temporary phase in normal development…. A most important finding [in a recent study] was that the fearful or anxious children, defined … as those with seven or more worries, did not seem to be in any particular psychological trouble.…Anxieties may be part of normal child development. — Science News, June 25, 1966
UPDATE
Actually, there is reason to worry about anxious children. Kids with anxiety disorders, depression or behavioral problems are especially likely to develop a range of difficulties as young adults, say researchers who conducted a long-term study published in 2015. The same goes for kids whose anxiety, mood or behavior issues cause daily problems but don’t qualify as psychiatric ailments. Problems that later dogged the study’s troubled youngsters, who grew up in rural North Carolina, included drug addiction, teenage parenthood, dropping out of high school and criminal arrests.