I don't think these two things necessarily go hand in hand. If the head of the executive branch should have absolute control over the branch, as the above user suggested, then if congress wants to control government agencies that are currently in the executive branch, those agencies should be placed outside of the executive into a different category that is either under the legislative branch or shared with the executive. In the status quo, all of the large government agencies being cut by DOGE are technically under the executive.

The Constitution does not provide for agencies in the legislative branch with power over the executive branch. Congress itself does have power over the executive, but mainly in that only it can pass laws, only it can raise revenue, only it can appropriate funds for expenditure, and, of course, only it can impeach executive officers and the president. Congress does not have the power to limit the president's executive orders to the executive branch agencies, for example.