For years, the most dangerous e-bikes were allowed, while smaller, safer ones — used by many parents to take their kids to school — were illegal. New regulations could change that.

For years, the most dangerous e-bikes were allowed, while smaller, safer ones — used by many parents to take their kids to school — were illegal. New regulations could change that.

The issue of e-bike scofflaws has grown considerably over the last few years, normally taking the form of teenagers on...