WASHINGTON—The top Democrat on the Senate’s tax-writing committee proposed taxing unrealized gains in investment assets every year at the same rates as other income, offering an idea that would transform how the U.S. taxes the wealthiest people.

The proposal from Sen. Ron Wyden of Oregon is the latest plan from Democratic lawmakers and presidential candidates for boosting taxes on the wealthy to address economic inequality and provide funding for their policy agenda. While this specific proposal has little chance of becoming...