When Congress sent states billions of dollars early in the coronavirus pandemic to help make schools safe, Tennessee Gov. Bill Lee saw an opportunity.

He used part of the windfall to further his goal of offering school choice options for parents, sending millions to charter schools that operate without traditional public oversight. That included funneling more than $4 million to new charters that are not scheduled to open until at least next year.

It was an easy way for the Republican governor to advance a long-held priority. For Lee and some other GOP governors, the discretionary money was a...